The position vector r → of a particle of mass m is given by the following equation r → t = α t 3 i ^ + β t 2 j ^ , where α = 10 3 m s - 3 , β = 5 m s - 2 and m = 0.1 kg . At t = 1 s , which of the following statements (s) is (are) true about the particle?

The torque τ → with respect to the origin is given by τ → = - 20 3 k ^ N m

The force F → is given by F → = i ^ + 2 j ^ N

One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q , at a height L above the hinge at point O . A block of weight α W is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of 2 2 W . Which of the following statement(s) is(are) correct?

The rope breaks if α > 1 . 5 .

The tension in the rope is 2 W for α = 0 . 5 .

A particle of mass M = 0 . 2 kg is initially at rest in the x y -plane at a point x = − l , y = − h , where l = 10 m and h = 1 m . The particle is accelerated at time t = 0 with a constant acceleration a = 10 m s - 2 along the positive x -direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by L → and τ → , respectively. i ^ , j ^ and k ^ are unit vectors along the positive x , y and z -directions, respectively. If k ^ = i ^ × j ^ then which of the following statement(s) is (are) correct?

L → = 4 k ^ when the particle passes through the point x = l , y = - h .

τ → = k ^ when the particle passes through the point x = 0 , y = - h .

A horizontal force F is applied at the centre of mass of a cylindrical object of mass m and radius R , perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is μ . The centre of mass of the object has an acceleration a . The acceleration due to gravity is g . Given that the object rolls without slipping, which of the following statement(s) is (are) correct?

For a thin-walled hollow cylinder, a = F 2 m .

For the same F , the value of a does not depend on whether the cylinder is solid or hollow.

The magnitude of the frictional force on the object due to the ground is always μ m g .

HARD

JEE Advanced

IMPORTANT

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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 $θ$ from the horizontal as shown in the figure below. The maximum value of $θ$ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)

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Important Questions on Rotational Motion

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Rotational Motion>JEE Advanced Paper 1 - 2020>Q 14

A small roller of diameter $20 cm$ has an axle of diameter $10 cm$ (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has moved $50 cm,$ the position of the scale will look like (figures are schematic and not drawn to scale)

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HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Rotational Motion>JEE Advanced Paper 1 - 2018>Q 15

Consider a body of mass

1.0 kg

at rest at the origin at time

t = 0

. A force

\vec{F} = (α t \hat{i} + β \hat{j})

is applied on the body, where

α = 1.0 {Ns}^{- 1}

and

β = 1.0 N

. The torque acting on the body about the origin at time

= 1.0 s

\vec{τ}

. Which of the following statements is (are) true?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Rotational Motion>JEE Advanced Paper 1 - 2018>Q 16

A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle

60 °

with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is

\frac{(2 - \sqrt{3})}{\sqrt{10}} s

, then the height of the top of the inclined plane (in meters) is __________. Take

g = 10 m s^{- 2}

MEDIUM

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Rotational Motion>JEE Advanced Paper 1 - 2017>Q 17

A block of mass

M

has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at

x = 0

, in a coordinate system fixed to the table. A point mass

m

is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block its position is

x

and velocity is

v

. At that instant, which of the following options is correct?
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HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Rotational Motion>JEE Advanced Paper 1 - 2016>Q 18

A uniform wooden stick of mass

1.6 kg

and length

l

rests in an inclined manner on a smooth, vertical wall of height h

(< l)

such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of

30^{o}

with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio

\frac{h}{l}

and the frictional force

f

at the bottom of the stick are:

(g = 10 m s^{- 2})

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Rotational Motion>JEE Advanced Paper 1 - 2016>Q 19

The position vector

\vec{r}

of a particle of mass

m

is given by the following equation

\vec{r} (t) = α t^{3} \hat{i} + β t^{2} \hat{j}, where α = \frac{10}{3} m s^{- 3}, β = 5 m s^{- 2} and m = 0.1 kg . At t = 1 s,

which of the following statements (s) is (are) true about the particle?

MEDIUM

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 6 - Rotational Motion>JEE Advanced Paper 1 - 2015>Q 21

A ring of mass

M

and radius

R

is rotating with angular speed

ω

about a fixed vertical axis passing through its centre O with two point masses each of mass

\frac{M}{8}

at rest at O. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is

\frac{8}{9} ω

and one of the masses is at a distance of

\frac{3}{5} R

from O. At this instant the distance of the other mass from O is

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Important Questions on Rotational Motion

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