## MCQ (Single Correct Answer)

The position vector of a particle related to time $t$ is given by
$\vec{r}=\left(10 t \hat{i}+15 t^{2} \hat{j}+7 \hat{k}\right) m$
The direction of ...

Three forces $$F_{1}=10 \mathrm{~N}, F_{2}=8 \mathrm{~N}, \mathrm{~F}_{3}=6 \mathrm{~N}$$ are acting on a particle of mass $$5 \mathrm{~kg}$$. The for...

A body of mass $$500 \mathrm{~g}$$ moves along $$\mathrm{x}$$-axis such that it's velocity varies with displacement $$\mathrm{x}$$ according to the re...

At any instant the velocity of a particle of mass $$500 \mathrm{~g}$$ is $$\left(2 t \hat{i}+3 t^{2} \hat{j}\right) \mathrm{ms}^{-1}$$. If the force a...

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $$30^\circ$$, with horizontal. Fo...

Figures (a), (b), (c) and (d) show variation of force with time.
The impulse is highest in figure....

A block of mass $$5 \mathrm{~kg}$$ is placed at rest on a table of rough surface. Now, if a force of $$30 \mathrm{~N}$$ is applied in the direction pa...

A body of mass $10 \mathrm{~kg}$ is moving with an initial speed of $20 \mathrm{~m} / \mathrm{s}$. The body stops after $5 \mathrm{~s}$ due to frictio...

As shown in figure, a $$70 \mathrm{~kg}$$ garden roller is pushed with a force of $$\vec{F}=200 \mathrm{~N}$$ at an angle of $$30^{\circ}$$ with horiz...

A block of $\sqrt{3} \mathrm{~kg}$ is attached to a string whose other end is attached to the wall. An unknown force $\mathrm{F}$ is applied so that t...

A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The val...

The time taken by an object to slide down 45$$^\circ$$ rough inclined plane is n times as it takes to slide down a perfectly smooth 45$$^\circ$$ incli...

A block of mass $m$ slides down the plane inclined at angle $$30^{\circ}$$ with an acceleration $$\frac{g}{4}$$. The value of coefficient of kinetic f...

Consider a block kept on an inclined plane (incline at 45$$^\circ$$) as shown in the figure. If the force required to just push it up the incline is 2...

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in fig...

As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g ...

Given below are two statements :
Statement I : An elevator can go up or down with uniform speed when its weight is balanced with the tension of its ca...

Two bodies of masses $$m_{1}=5 \mathrm{~kg}$$ and $$m_{2}=3 \mathrm{~kg}$$ are connected by a light string going over a smooth light pulley on a smoot...

A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length 'l' ...

A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $$\theta$$. The...

A block 'A' takes 2 s to slide down a frictionless incline of 30$$^\circ$$ and length 'l', kept inside a lift going up with uniform velocity 'v'. If t...

A bag is gently dropped on a conveyor belt moving at a speed of $$2 \mathrm{~m} / \mathrm{s}$$. The coefficient of friction between the conveyor belt ...

Two masses $$M_{1}$$ and $$M_{2}$$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the m...

Three masses $$M=100 \mathrm{~kg}, \mathrm{~m}_{1}=10 \mathrm{~kg}$$ and $$\mathrm{m}_{2}=20 \mathrm{~kg}$$ are arranged in a system as shown in figur...

A monkey of mass $$50 \mathrm{~kg}$$ climbs on a rope which can withstand the tension (T) of $$350 \mathrm{~N}$$. If monkey initially climbs down with...

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at w...

A 2 kg block is pushed against a vertical wall by applying a horizontal force of 50 N. The coefficient of static friction between the block and the wa...

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley...

A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal to one-fourth of its weight on the flo...

A block of mass 2 kg moving on a horizontal surface with speed of 4 ms$$-$$1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding...

A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two ...

A person is standing in an elevator. In which situation, he experiences weight loss?

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the mot...

A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms$$-$$1. The coefficient of friction between the surface and block ...

A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to t...

An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following s...

Statement : 1If three forces $${\overrightarrow F _1},{\overrightarrow F _2}$$ and $${\overrightarrow F _3}$$ are represented by three sides of a tria...

The boxes of masse 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strik...

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms-2. The g...

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $...

A force $$\overrightarrow F = (40\widehat i + 10\widehat j)N$$ acts on a body of mass 5 kg. If the body starts from rest, its position vector $$\over...

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with...

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle $$\theta$$ as shown in figure. The coefficient of kin...

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts mo...

A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance f...

A particle moving in the xy plane experiences a velocity dependent force
$$\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)$$
...

An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts
slipping after it is at height h from the bottom....

A spaceship in space sweeps stationary
interplanetary dust. As a result, its mass
increases at a rate $${{dM\left( t \right)} \over {dt}}$$ = bv2(t), ...

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a
resistive force mkv2
where v is its speed. The maximu...

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied
horizontally at the mid point of the rope such that the t...

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an
angle of 30o with the horizontal, as shown ...

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched
lengths l1 and l2 where, l1 = nl2 and ...

A bullet of mass 20 g has an initial speed of 1 ms–1
, just before it starts penetrating a mud wall of thickness
20 cm. If the wall offers a mean resi...

Two blocks A and B of masses mA = 1 kg and mB = 3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and ...

A ball is thrown upward with an initial velocity
V0 from the surface of the earth. The motion
of the ball is affected by a drag force equal to
m$$\gam...

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external...

Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle $$\theta $$ with each other. If the force Q is doubled, then their resultant...

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point. the rope deviated at an...

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static fric...

Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible
string over a frictionless pulley, are moving as shown in the figure. The
coefficien...

A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of $${30^o}$$. The external force required to ...

A given object takes n times more time to slide down a $${45^ \circ }$$ rough inclined plane as it takes to slide down a perfectly smooth $${45^ \circ...

A particle of mass m is acted upon by a force F given by the empirical law
F =$${R \over {{t^2}}}\,v\left( t \right).$$ If this law is to be tested ...

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the
gravitational acceleration. On an inclined plane inside the roc...

Given in the figure are two blocks $$A$$ and $$B$$ of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force $$F$$ as ...

A block of mass $$m$$ is placed on a surface with a vertical cross section given by $$y = {{{x^3}} \over 6}.$$ If the coefficient of friction is $$0.5...

A particle of mass $$m$$ is at rest at the origin at time $$t=0.$$ It is subjected to a force $$F\left( t \right) = {F_0}{e^{ - bt}}$$ in the $$x$$ di...

Two fixed frictionless inclined planes making an angle $${30^ \circ }$$ and $${60^ \circ }$$ with the vertical are shown in the figure. Two blocks $$A...

A block of mass $$m$$ is connected to another block of $$mass$$ $$M$$ by a spring (massless) of spring constant $$k.$$ The block are kept on a smooth ...

A smooth block is released at rest on a $${45^ \circ }$$ incline and then slides a distance $$'d'$$. The time taken to slide is $$'n'$$ times as much ...

A particle of mass 0.3 kg subjected to a force $$F=-kx$$ with $$k=15$$ $$N/m$$. What will be its initial acceleration if it is released from a point 2...

Consider a car moving on a straight road with a speed of $$100$$ $$m/s$$. The distance at which car can be stopped is $$\left[ {{\mu _k} = 0.5} \right...

A block is kept on a frictionless inclined surface with angle of inclination $$'\,\alpha \,'.$$ The incline is given an acceleration $$a$$ to keep the...

Two masses $${m_1} = 5kg$$ and $${m_2} = 4.8kg$$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses...

A block rests on a rough inclined plane `making an angle of $${30^ \circ }$$ with the horizontal. The coefficient of static friction between the block...

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $$49$$ $$N,$$ when the lift is stationar...

A light spring balance hangs from the hook of the other light spring balance and a block of mass $$M$$ $$kg$$ hangs from the former one. Then the true...

A marble block of mass $$2$$ $$kg$$ lying on ice when given a velocity of $$6$$ $$m/s$$ is stopped by friction in $$10$$ $$s.$$ Then the coefficient o...

A block of mass $$M$$ is pulled along a horizontal frictionless surface by a rope of mass $$m.$$ If a force $$P$$ is applied at the free end of the ro...

A rocket with a lift-off mass $$3.5 \times {10^4}\,\,kg$$ is blasted upwards with an initial acceleration of $$10m/{s^2}.$$ Then the initial thrust of...

Three forces start acting simultaneously on a particle moving with velocity, $$\overrightarrow v \,\,.$$ These forces are represented in magnitude and...

A horizontal force of $$10$$ $$N$$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the ...

A lift is moving down with acceleration $$a.$$ A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in ...

When forces $${F_1},\,\,{F_2},\,\,{F_3}$$ are acting on a particle of mass $$m$$ such that $${F_2}$$ and $${F_3}$$ are mutually perpendicular, then th...

Two forces are such that the sum of their magnitudes is $$18$$ $$N$$ and their resultant is $$12$$ $$N$$ which is perpendicular to the smaller force. ...

A light string passing over a smooth light pulley connects two blocks of masses $${m_1}$$ and $${m_2}$$ (vertically). If the acceleration of the syste...

Three identical blocks of masses $$m=2$$ $$kg$$ are drawn by a force $$F=10.2$$ $$N$$ with an acceleration of $$0.6$$ $$m{s^{ - 2}}$$ on a frictionles...

One end of a mass-less rope, which passes over a mass-less and friction-less pulley $$P$$ is tied to a hook $$C$$ while the other end is free. Maximum...

## Numerical

Four forces are acting at a point $$\mathrm{P}$$ in equilibrium as shown in figure. The ratio of force $$\mathrm{F}_{1}$$ to $$\mathrm{F}_{2}$$ is $$1...

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a...

A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal d...

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth ta...

A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F = $$\sqrt{x}$$N as shown in figure.
The ...

A force on an object of mass 100 g is $$\left( {10\widehat i + 5\widehat j} \right)$$ N. The position of that object at t = 2 s is $$\left( {a\widehat...

When a body slides down from rest along a smooth inclined plane making an angle of 30$$^\circ$$ with the horizontal, it takes time T. When the same bo...

A car is moving on a plane inclined at 30$$^\circ$$ to the horizontal with an acceleration of 10 ms$$-$$2 parallel to the plane upward. A bob is suspe...

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blo...

A body of mass 'm' is launched up on a rough inclined plane making an angle of 30$$^\circ$$ with the horizontal. The coefficient of friction between t...

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bul...

A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum ...

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction $${1 \over {\sqrt 3 }}$$. It is desired to make the...

Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between ...

A body of mass 2 kg moves under a force of $$\left( {2\widehat i + 3\widehat j + 5\widehat k} \right)$$N. It starts from rest and was at the origin in...

A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward ac...

A boy pushes a box of mass 2 kg with a force $$\overrightarrow F = \left( {20\widehat i + 10\widehat j} \right)N$$ on a frictionless surface. If the ...

As shown in the figure, a block of mass $$\sqrt 3 $$ kg is kept on a horizontal rough surface of coefficient of friction $${1 \over {3\sqrt 3 }}$$. Th...

An inclined plane is bent in such a way that the vertical cross-section is given by $$y = {{{x^2}} \over 4}$$ where y is in vertical and x in horizont...

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that shou...