Laws of Motion — JEE Advanced PYQs

A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg. Suppose that the variation of the height $y$ (in m) of the elevator, from the ground, with time $t$ (in s) is given by $y=8\left[1+\sin \left(\frac{2\pi t}{T}\right)\right]$, w …

A projectile of mass 200 g is launched in a viscous medium at an angle 60° with the horizontal, with an initial velocity of 270 m/s. It experiences a viscous drag force $\vec{F}=-c\vec{v}$ where the drag coefficient $c=0.1$ kg/s and $\vec{v}$ is the instantaneous velocity …

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 fing …

A student skates up a ramp that makes an angle 30° with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed $v_0$ and wants to turn around over a semicircular path xyz of radius $R$ during which he/she reaches a maximum height $h$ (at point …

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 ${\mathrm{a}}_1$, ${\mathrm{a}}_2$ and ${\mathrm{a}}_3$ as …

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m=0.4kg$ is at rest on this surface. An impulse of $1.0Ns$ is applied to the block at time $t=0$ so that it starts moving along the $x$-axis with a velocity …

The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V(r)=k{r}^2/2$, where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $R$ about the point $O$. If $v$ is the speed o …

PARAGRAPH 1

A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $\omega$ is an example of …

PARAGRAPH 1

A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $\omega$ is an example of …

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the vari …

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 figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves fr …

A block of mass $m_1=1kg$ another mass $m_2=2kg$, 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 $m_1$ and the plane is alway …

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 …

A small block of mass of 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 center of mass as shown in the figure. The block remains stationary if ( take …

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) …

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 …

A train is moving along a straight line with a constant acceleration ' $a$ '. A boy standing in the train throws a ball forward with a speed of $10\mathrm{m}/\mathrm{s}$, at an angle of $60^{\circ }$ to the horizontal. The boy has to move forward by 1.15 m inside the tra …

A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta >\mu$. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plan …

A piece of wire is bent in the shape of a parabola $y=k{x}^2$ ( $y$-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 …

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg . Taking $g=10\mathrm{m}/{\mathrm{s}}^2$, find the work done (in joules) by the string on the block of mass 0.36 kg during the first sec …

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 $\theta$ of this inclined plane from the horizontal plane is gradually increased from $0^{\circ }$. Then

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.

STATEMENT-1
A block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same b …

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

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.

Two blocks A and B of masses 2m and m, respectively, are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively

A circular disc with a groove along its diameter is placed horizontally. A block of mass 1 kg is placed as shown. The co-efficient of friction between the block and all surfaces of groove in contact is $\mu =2/5$. The disc has an acceleration of $25$ m/s${}^2$. Find the acce …