Laws of Motion · Physics · JEE Advanced

MCQ (Single Correct Answer)

A particle of mass $m$ is moving in the $x y$-plane such that its velocity at a point $(x, y)$ is given as $\overrightarrow{\mathrm{v}}=\alpha(y \hat{x}+2 x \hat{y})$, where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?

JEE Advanced 2023 Paper 2 Online

A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle $$\theta $$ from the horizontal as shown in the figure below. The maximum value of $$\theta $$ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)

JEE Advanced 2020 Paper 1 Offline

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the below figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

JEE Advanced 2014 Paper 2 Offline

A block of mass m₁ = 1 kg another mass m₂ = 2 kg, are placed together (see figure) on an inclined plane with angle of inclination $$\theta$$. Various values of $$\theta$$ are given in List I. The coefficient of friction between the block m₁ and the plane is always zero. The coefficient of static and dynamic friction between the block m₂ and the plane are equal to $$\mu$$ = 0.3. In List II expressions for the friction on the block m₂ are given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option. The acceleration due to gravity is denoted by g.

[Useful information : tan (5.5$$^\circ$$) $$\approx$$ 0.1; tan (11.5$$^\circ$$) $$\approx$$ 0.2; tan (16.5$$^\circ$$) $$\approx$$ 0.3]

List I		List II
P.	$$\theta = 5^\circ $$	1.	$${m_2}g\sin \theta $$
Q.	$$\theta = 10^\circ $$	2.	$$({m_1} + {m_2})g\sin \theta $$
R.	$$\theta = 15^\circ $$	3.	$$\mu {m_2}g\cos \theta $$
S.	$$\theta = 20^\circ $$	4.	$$\mu ({m_1} + {m_2})g\cos \theta $$

JEE Advanced 2014 Paper 2 Offline

A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is

IIT-JEE 2011 Paper 1 Offline

A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P₁ = mg(sinθ − μ cosθ) to P₂ = mg(sinθ + μ cosθ), the frictional force f versus P graph will look like

IIT-JEE 2010 Paper 1 Offline

A piece of wire is bent in the shape of a parabola y = kx² (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration $$a$$. The distance of the new equilibrium position of the bead, where the bead can stays at rest with respect to the wire, from the y-axis is

IIT-JEE 2009 Paper 2 Offline

A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is $$\sqrt 3 $$. The inclination θ of this inclined plane from the horizontal plane is gradually increased from $$0^\circ $$. Then

IIT-JEE 2009 Paper 1 Offline

STATEMENT 1 : It is easier to pull a heavy object than to push it on a level ground.

and

STATEMENT 2 : The magnitude of frictional force depends on the nature of the two surfaces in contact.

IIT-JEE 2008 Paper 2 Offline

The speed of the block at point B immediately after it strikes the second incline is

IIT-JEE 2008 Paper 1 Offline

The speed of the block at point C, immediately before it leaves the second incline is

IIT-JEE 2008 Paper 1 Offline

A particle moves in the X - Y plane under the influence of a force such that its linear momentum is $$\overrightarrow p \left( t \right) = A\left[ {\widehat i\cos (kt) - \widehat j\sin (kt)} \right]$$, where A and k are constants. The angle between the force and the momentum is

IIT-JEE 2007 Paper 2 Offline

STATEMENT 1

A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.

Because

STATEMENT 2

For every action there is an equal and opposite reaction.

IIT-JEE 2007 Paper 2 Offline

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $$\theta $$ should be

IIT-JEE 2001 Screening

A block of mass 0.1 is held against a wall applying a horizontal force of 5 N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is:

IIT-JEE 1994

A ship of mass 3 $$ \times $$ 10⁷ kg initially at rest, is pulled by a force of 5 $$ \times $$ 10⁴ N through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is

IIT-JEE 1980

A block of mass 2 kg rests on a rough inclined plane making an angle of $$30^\circ $$ with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is

IIT-JEE 1980

Numerical

A projectile is thrown from a point O on the ground at an angle 45$$^\circ$$ from the vertical and with a speed 5$$\sqrt 2 $$ m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, t seconds after splitting, falls to the ground at a distance x meters from the point O. The acceleration due to gravity g = 10 m/s².

The value of t is _____________.

JEE Advanced 2021 Paper 1 Online

Put a uniform meter scale horizontally on your extended index fingers with the left one at 0.00 cm and the right one at 90.00 cm. When you attempt to move both the fingers slowly towards the center, initially only the left finger slips with respect to the scale and the right finger does not. After some distance, the left finger stops and the right one starts slipping. Then the right finger stops at a distance x_R from the center (50.00 cm) of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are 0.40 and 0.32, respectively, the value of x_R (in cm) is ______.

JEE Advanced 2020 Paper 1 Offline

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $$m=0.4$$ $$kg$$ is at rest on this surface. An impulse of $$1.0$$ $$Ns$$ is applied to the block at time $$t=0$$ so that it starts moving along the $$x$$-axis with a velocity $$v\left( t \right) = {v_0}{e^{ - t/\tau }},$$ where $${v_0}$$ is a constant and $$\tau = 4s.$$ The displacement of the block, in metres, at $$t = \tau $$ is ______________ Take $${e^{ - 1}} = 0.37.$$

JEE Advanced 2018 Paper 2 Offline

A block is moving on an inclined plane making an angle $$45^\circ $$ with the horizontal and the coefficient of friction is $$\mu $$. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 $$\mu $$, then N is

IIT-JEE 2011 Paper 1 Offline

MCQ (More than One Correct Answer)

A block of mass 2M is attached to a massless spring with spring-constant k.This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are a₁, a₂ and a₃ as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is x₀. Which of the following option(s) is/are correct? [g is the acceleration due to gravity. Neglect friction]

JEE Advanced 2019 Paper 2 Offline

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $$\theta$$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $$\mu$$₁ and that between the floor and the ladder is $$\mu$$₂. The normal reaction of the wall on the ladder is N₁ and that of the floor is N₂. If the ladder is about to slip, then

JEE Advanced 2014 Paper 1 Offline

A small block of mass 0.1 kg lies on a fixed inclined plane PQ which makes an angle $$\theta$$ with the horizontal. A horizontal force of 1 N acts on the block through its centre of mass as shown in the figure. The block remains stationary if (take g = 10 m/s²)