## Numerical

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A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in vertical pla...
JEE Main 2021 (Online) 1st September Evening Shift
In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case ...
JEE Main 2021 (Online) 27th July Evening Shift
A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its...
JEE Main 2021 (Online) 25th July Evening Shift
A particle of mass 'm' is moving in time 't' on a trajectory given by$$\overrightarrow r = 10\alpha {t^2}\widehat i + 5... JEE Main 2021 (Online) 25th July Morning Shift The centre of a wheel rolling on a plane surface moves with a speed v0. A particle on the rim of the wheel at the same l... JEE Main 2021 (Online) 22th July Evening Shift A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations... JEE Main 2021 (Online) 20th July Evening Shift Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii ... JEE Main 2021 (Online) 20th July Evening Shift A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes ti... JEE Main 2021 (Online) 20th July Morning Shift The following bodies,(1) a ring(2) a disc(3) a solid cylinder(4) a solid sphere,of same mass 'm' and radius 'R' are allo... JEE Main 2021 (Online) 17th March Morning Shift The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the t... JEE Main 2021 (Online) 17th March Morning Shift A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle$$\theta$$with... JEE Main 2021 (Online) 16th March Evening Shift Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force$$\overrig...
JEE Main 2021 (Online) 16th March Morning Shift
Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The ...
JEE Main 2021 (Online) 16th March Morning Shift
A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minim...
JEE Main 2021 (Online) 25th February Morning Slot
A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about...
JEE Main 2021 (Online) 24th February Evening Slot
The centre of mass of solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then value of x is _____...
JEE Main 2020 (Online) 6th September Evening Slot
A force $$\overrightarrow F = \left( {\widehat i + 2\widehat j + 3\widehat k} \right)$$ N acts at a point $$\left( {4\w... JEE Main 2020 (Online) 5th September Morning Slot A circular disc of mass M and radius R is rotating about its axis with angular speed$${\omega _1}$$. If another statio... JEE Main 2020 (Online) 4th September Morning Slot An massless equilateral triangle EFG of side ‘a’ (As shown in figure) has three particles of mass m situated at its vert... JEE Main 2020 (Online) 3rd September Evening Slot A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolut... JEE Main 2020 (Online) 3rd September Morning Slot A square shaped hole of side l =$${a \over 2}$$is carved out at a distance d =$${a \over 2}$$from the centre ‘O’ of ... JEE Main 2020 (Online) 2nd September Evening Slot A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s–1) with w... JEE Main 2020 (Online) 9th January Morning Slot One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from rest when it makes an angl... JEE Main 2020 (Online) 9th January Morning Slot Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a... JEE Main 2020 (Online) 7th January Evening Slot ## MCQ (Single Correct Answer) More A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance be... JEE Main 2021 (Online) 31st August Evening Shift Two discs have moments of inertia I1 and I2 about their respective axes perpendicular to the plane and passing through t... JEE Main 2021 (Online) 27th August Evening Shift A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a bo... JEE Main 2021 (Online) 27th August Morning Shift The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the m... JEE Main 2021 (Online) 26th August Evening Shift Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Mom... JEE Main 2021 (Online) 25th July Morning Shift Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without s... JEE Main 2021 (Online) 22th July Evening Shift A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic... JEE Main 2021 (Online) 20th July Evening Shift Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpend... JEE Main 2021 (Online) 18th March Evening Shift A particle of mass m moves in a circular orbit under the central potential field,$$U(r) = - {C \over r}$$, where C is ... JEE Main 2021 (Online) 18th March Evening Shift A thin circular ring of mass M and radius r is rotating about its axis with an angular speed$$\omega$$. Two particles h... JEE Main 2021 (Online) 18th March Morning Shift A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady... JEE Main 2021 (Online) 17th March Morning Shift The maximum and minimum distances of a comet from the Sun are 1.6$$\times$$1012 m and 8.0$$\times$$1010 m respective... JEE Main 2021 (Online) 16th March Morning Shift A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 ... JEE Main 2021 (Online) 16th March Morning Shift A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of iner... JEE Main 2021 (Online) 26th February Evening Shift A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fi... JEE Main 2021 (Online) 26th February Morning Shift Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a squa... JEE Main 2021 (Online) 26th February Morning Shift A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v0. It encounters an inclined pla... JEE Main 2021 (Online) 25th February Evening Shift A circular hole of radius$$\left( {{a \over 2}} \right)$$is cut out of a circular disc of radius 'a' as shown in figur... JEE Main 2021 (Online) 24th February Evening Slot Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as; I1 = M.I. of thin circular ring ... JEE Main 2021 (Online) 24th February Morning Slot The linear mass density of a thin rod AB of length L varies from A to B as$$\lambda \left( x \right) = {\lambda _0}\lef...
JEE Main 2020 (Online) 6th September Evening Slot
A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in uni...
JEE Main 2020 (Online) 6th September Morning Slot
A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is fa...
JEE Main 2020 (Online) 6th September Morning Slot
Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its top, R and height...
JEE Main 2020 (Online) 6th September Morning Slot
Four point masses, each of mass m, are fixed at the corners of a square of side $$l$$. The square is rotating with angul...
JEE Main 2020 (Online) 6th September Morning Slot
A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T1 and, (ii)...
JEE Main 2020 (Online) 5th September Evening Slot
A wheel is rotating freely with an angular speed $$\omega$$ on a shaft. The moment of inertia of the wheel is I and the...
JEE Main 2020 (Online) 5th September Morning Slot
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the...
JEE Main 2020 (Online) 4th September Evening Slot
Consider two uniform discs of the same thickness and different radii R1 = R and R2 = $$\alpha$$R made of the same mat...
JEE Main 2020 (Online) 4th September Evening Slot
A uniform rod of length ‘$$l$$’ is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft r...
JEE Main 2020 (Online) 3rd September Evening Slot
Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicu...
JEE Main 2020 (Online) 3rd September Morning Slot
Two uniform circular discs are rotating independently in the same direction around their common axis passing through the...
JEE Main 2020 (Online) 2nd September Evening Slot
A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a &lt; R) by applying a force F at it...
JEE Main 2020 (Online) 2nd September Morning Slot
A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx2 and rotating with angular spe...
JEE Main 2020 (Online) 2nd September Morning Slot
A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A ma...
JEE Main 2020 (Online) 9th January Evening Slot
A rod of length L has non-uniform linear mass density given by $$\rho$$(x) = $$a + b{\left( {{x \over L}} \right)^2}$$ ...
JEE Main 2020 (Online) 9th January Evening Slot
A spring mass system (mass m, spring constant k and natural length $$l$$) rest in equilibrium on a horizontal disc. The ...
JEE Main 2020 (Online) 9th January Evening Slot
Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an...
JEE Main 2020 (Online) 9th January Morning Slot
A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of...
JEE Main 2020 (Online) 8th January Evening Slot
As shown in figure, when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (cent...
JEE Main 2020 (Online) 8th January Evening Slot
A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length $$\ell$$. The...
JEE Main 2020 (Online) 8th January Morning Slot
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the...
JEE Main 2020 (Online) 8th January Morning Slot
Consider a uniform rod of mass M = 4m and length $$\ell$$ pivoted about its centre. A mass m moving with velocity v mak...
JEE Main 2020 (Online) 8th January Morning Slot
Mass per unit area of a circular disc of radius $$a$$ depends on the distance r from its centre as $$\sigma \left( r \ri... JEE Main 2020 (Online) 7th January Evening Slot Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides... JEE Main 2020 (Online) 7th January Morning Slot The radius of gyration of a uniform rod of length$$l$$, about an axis passing through a point$${l \over 4}$$away from... JEE Main 2020 (Online) 7th January Morning Slot A smooth wire of length 2$$\pi $$r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the ... JEE Main 2019 (Online) 12th April Evening Slot A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude$$\theta $$0. If the person... JEE Main 2019 (Online) 12th April Morning Slot A uniform rod of length$$\ell $$is being rotated in a horizontal plane with a constant angular speed about an axis pas... JEE Main 2019 (Online) 12th April Morning Slot A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc var... JEE Main 2019 (Online) 12th April Morning Slot A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The syst... JEE Main 2019 (Online) 10th April Evening Slot Two coaxial discs, having moments of inertia I1 and I1/2, are rotating with respective angular velocities$$\omega $$1 ... JEE Main 2019 (Online) 10th April Morning Slot A thin smooth rod of length L and mass M is rotating freely with angular speed$$\omega $$0 about an axis perpendicular ... JEE Main 2019 (Online) 9th April Evening Slot Moment of inertia of a body about a given axis is 1.5 kg m2. Initially the body is at rest. In order to produce a rotati... JEE Main 2019 (Online) 9th April Evening Slot A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a f... JEE Main 2019 (Online) 9th April Morning Slot A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height ... JEE Main 2019 (Online) 8th April Evening Slot An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is ... JEE Main 2019 (Online) 8th April Evening Slot A thin circular plate of mass M and radius R has its density varying as$$\rho $$(r) =$$\rho $$0r with$$\rho $$0 as co... JEE Main 2019 (Online) 8th April Morning Slot Four particles A, B, C and D with masses mA = m, mB = 2m, mC = 3m and mD = 4m are at the corners of a square. They have ... JEE Main 2019 (Online) 8th April Morning Slot A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liqu... JEE Main 2019 (Online) 12th January Evening Slot Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed$$\omega $$. At t = ... JEE Main 2019 (Online) 12th January Evening Slot The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I(x)... JEE Main 2019 (Online) 12th January Evening Slot Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its ax... JEE Main 2019 (Online) 12th January Morning Slot A string is wound around a hollow cylinder of mass 5 kg and radius 0.5m. If the string is now pulled with a horizontal f... JEE Main 2019 (Online) 11th January Evening Slot A circular disc D1 of mass M and radius R has two identical discs D2 and D3 of the same mass M and radius R attached rig... JEE Main 2019 (Online) 11th January Evening Slot The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the... JEE Main 2019 (Online) 11th January Evening Slot An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid-points of its si... JEE Main 2019 (Online) 11th January Morning Slot A slab is subjected to two forces$$\overrightarrow {{F_1}} $$and$$\overrightarrow {{F_2}} $$of same magnitude F as ... JEE Main 2019 (Online) 11th January Morning Slot A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change in velo... JEE Main 2019 (Online) 11th January Morning Slot Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see fi... JEE Main 2019 (Online) 10th January Evening Slot A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assumi... JEE Main 2019 (Online) 10th January Morning Slot To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rot... JEE Main 2019 (Online) 10th January Morning Slot A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30o from the horizontal as sho... JEE Main 2019 (Online) 9th January Evening Slot If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the S... JEE Main 2019 (Online) 9th January Morning Slot An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC... JEE Main 2019 (Online) 9th January Morning Slot A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes w... JEE Main 2018 (Online) 16th April Morning Slot A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released... JEE Main 2018 (Online) 15th April Evening Slot A thin uniform bar of length$$L$$and mass$$8$$m lies on a smooth horizontal table. Two point masses m and 2 m are mo... JEE Main 2018 (Online) 15th April Evening Slot A uniform rod$$AB$$is suspended from a point$$X,$$at a variable distance$$x$$from$$A$$, as shown, To make the ro... JEE Main 2018 (Online) 15th April Morning Slot From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The ... JEE Main 2018 (Offline) Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of iner... JEE Main 2018 (Offline) A circular hole of radius$${R \over 4}$$is made in a thin uniform disc having mass M and radius R, as shown in figure... JEE Main 2017 (Online) 9th April Morning Slot The machine as shown has 2 rods of length1 m connected by a pivot at the top. The end of one rod is connected to the flo... JEE Main 2017 (Online) 9th April Morning Slot A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body... JEE Main 2017 (Online) 8th April Morning Slot In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes ... JEE Main 2017 (Online) 8th April Morning Slot Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular... JEE Main 2017 (Online) 8th April Morning Slot A slender uniform rod of mass M and length$$l$$is pivoted at one end so that it can rotate in a vertical plane (see fi... JEE Main 2017 (Offline) The moment of inertia of a uniform cylinder of length$$l$$and radius R about its perpendicular bisector is$$I$$. What... JEE Main 2017 (Offline) In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then$${{BC} \over {...
JEE Main 2016 (Online) 10th April Morning Slot
Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, ...
JEE Main 2016 (Online) 10th April Morning Slot
A cubical block of side 30 cm is moving with velocity 2 ms−1 on a smooth horizontal surface. The surface has a bump at a...
JEE Main 2016 (Online) 9th April Morning Slot
A roller is made by joining together two cones at their vertices $$0$$. It is kept on two rails $$AB$$ and $$CD$$, which...
JEE Main 2016 (Offline)
From a solid sphere of mass $$M$$ and radius $$R$$ a cube of maximum possible volume is cut. Moment of inertia of cube a...
JEE Main 2015 (Offline)
Distance of the center of mass of a solid uniform cone from its vertex is $$z{}_0$$. If the radius of its base is $$R$$ ...
JEE Main 2015 (Offline)
A mass $$'m'$$ is supported by a massless string wound around a uniform hollow cylinder of mass $$m$$ and radius $$R.$$ ...
JEE Main 2014 (Offline)
A bob of mass $$m$$ attached to an inextensible string of length $$l$$ is suspended from a vertical support. The bob rot...
JEE Main 2014 (Offline)
A hoop of radius $$r$$ and mass $$m$$ rotating with an angular velocity $${\omega _0}$$ is placed on a rough horizontal ...
JEE Main 2013 (Offline)
A pulley of radius $$2$$ $$m$$ is rotated about its axis by a force $$F = \left( {20t - 5{t^2}} \right)$$ newton (where ...
AIEEE 2011
A mass $$m$$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $$m... AIEEE 2011 A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a ... AIEEE 2011 A thin uniform rod of length$$l$$and mass$$m$$is swinging freely about a horizontal axis passing through its end. It... AIEEE 2009 A thin rod of length$$'L'$$is lying along the$$x$$-axis with its ends at$$x=0$$and$$x=L$$. Its linear density (mas... AIEEE 2008 Consider a uniform square plate of side$$' a '$$and mass$$'m'$$. The moment of inertia of this plate about an axis pe... AIEEE 2008 For the given uniform square lamina$$ABCD$$, whose center is$$O,$$... AIEEE 2007 Angular momentum of the particle rotating with a central force is constant due to AIEEE 2007 A round uniform body of radius$$R,$$mass$$M$$and moment of inertia$$I$$rolls down (without slipping) an inclined p... AIEEE 2007 A circular disc of radius$$R$$is removed from a bigger circular disc of radius$$2R$$such that the circumferences of ... AIEEE 2007 A force of$$ - F\widehat k$$acts on$$O,$$the origin of the coordinate system. The torque about the point$$(1, -1)$... AIEEE 2006 Four point masses, each of value $$m,$$ are placed at the corners of a square $$ABCD$$ of side $$l$$. The moment of iner... AIEEE 2006 A thin circular ring of mass $$m$$ and radius $$R$$ is rotating about its axis with a constant angular velocity $$\omega... AIEEE 2006 Consider a two particle system with particles having masses$${m_1}$$and$${m_2}$$. If the first particle is pushed tow... AIEEE 2006 A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force$$'\,\,\overrightarrow F \,\,... AIEEE 2005 A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity breaks into two-parts; a body $$B$$ of mass ... AIEEE 2005 The moment of inertia of a uniform semicircular disc of mass $$M$$ and radius $$r$$ about a line perpendicular to the pl... AIEEE 2005 An annular ring with inner and outer radii $${R_1}$$ and $${R_2}$$ is rolling without slipping with a uniform angular sp... AIEEE 2005 A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which on of the fol... AIEEE 2004 One solid sphere $$A$$ and another hollow sphere $$B$$ are of same mass and same outer radii. Their moment of inertia ab... AIEEE 2004 A circular disc $$X$$ of radius $$R$$ is made from an iron plate of thickness $$t,$$ and another disc $$Y$$ of radius$...
AIEEE 2003
Let $$\overrightarrow F$$ be the force acting on a particle having position vector $$\overrightarrow r ,$$ and $$\over... AIEEE 2003 A particle performing uniform circular motion has angular frequency is doubled &amp; its kinetic energy halved, then the... AIEEE 2003 Moment of inertia of a circular wire of mass$$M$$and radius$$R$$about its diameter is AIEEE 2002 Two identical particles move towards each other with velocity$$2v$$and$$v$$respectively. The velocity of center of m... AIEEE 2002 A particle of mass$$m$$moves along line PC with velocity$$v$$as shown. What is the angular momentum of the particle ... AIEEE 2002 A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide ... AIEEE 2002 Initial angular velocity of a circular disc of mass$$M$$is$${\omega _1}.$$Then two small spheres of mass$$m are a...
AIEEE 2002

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