Rolling Motion

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JEE Main 2021, 22 July Shift-II

The centre of a wheel rolling on a plane surface moves with a speed $v_{0}$ . A particle on the rim of the wheel at the same level as the centre will be moving at a speed $x v_{0}$ . Then, the value of $x$ is ……… .

JEE Main 2019, 10 Jan Shift-I

A homogeneous solid cylindrical roller of radius $R$ and mass $m$ is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is

\frac{F}{2 m R}

(B)

\frac{2 F}{3 m R}

(C)

\frac{3 F}{2 m R}

(D)

\frac{F}{3 m R}

JEE Main 2021 (20 July Shift-II)

LEVELJEE Main

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $\frac{x}{2}$ . Then, the value of $x$ is …… .

LEVELJEE Main

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane : (i) a ring of radius $R$ , (ii) a solid cylinder of radius $R /2$ and (iii) a solid sphere of radius $R /4$ . If in each case, the speed of the centre of mass at the bottom of the incline is same, the ratio of the maximum height they climb is

(A)

10 : 15 : 7

(B)

4 : 3 : 2

(C)

14 : 15 : 20

(D)

2 : 3 : 4

JEE Main 2021, 17 March Shift-II

LEVELJEE Advanced

A sphere of mass $2 kg$ and radius $0.5 m$ is rolling with an initial speed of $1 ms^{- 1}$ goes up an inclined plane which makes an angle of $3 0^{\circ}$ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A ?

(A)

0.60 s

(B)

0.52 s

(C)

0.57 s

(D)

0.80 s

JEE Main 2021

LEVELJEE Main

A circular disc reaches from top to bottom of an inclined plane of length $L$ . When it slips down the plane, it takes time $t_{1}$ . When it rolls down the plane, it takes time $t_{2}$ . The value of $\frac{t _{2}}{t _{1}}$ is $\frac{3}{x}$ . The value of $x$ will be …… .

JEE Main 2021

LEVELJEE Main

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is $50%$ of its translational kinetic energy. The body is

JEE Main 2021, 22 July Shift-II

LEVELJEE Main

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation.

(A)

The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.

(B)

The ring has the greatest and the cylinder has the least velocity of the centre of mass at the bottom of the inclined plane.

(C)

All of them will have same velocity.

(D)

The cylinder has the greatest and the sphere has the least velocity of the centre of mass at the bottom of the inclined plane.

JEE Main 2021, 16 March Shift-II

LEVELJEE Main

A solid disc of radius $a$ and mass $m$ rolls down without slipping on an inclined plane making an angle $θ$ with the horizontal. The acceleration of the disc will be $\frac{2}{b} g sin θ$ , where $b$ is ……… . (Round off to the nearest integer) ( $g = acceleration due to gravity$ ) ( $θ = angle as shown in figure$ )

JEE Main 2019, 8 April Shift-II

LEVELJEE Advanced

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The ratio $\frac{h _{sph}}{h _{cyl}}$ is given by

(A)

\frac{2}{5}

(B)

\frac{14}{15}

(C)

1

(D)

\frac{4}{5}

JEE Main 2020, 8 Jan Shift-II

LEVELJEE Main

A uniform sphere of mass $500 g$ rolls without slipping on a plane horizontal surface with its centre moving at a speed of $5.00 cm/s$ . Its kinetic energy is

(A)

6.25 \times 1 0^{- 4} J

(B)

1.13 \times 1 0^{- 3} J

(C)

8.75 \times 1 0^{- 4} J

(D)

8.75 \times 1 0^{- 3} J

JEE Main 2021, 17 March Shift-I

LEVELJEE Main

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 allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ……… . (Mark the body as per their respective numbering given in the question)

LEVELJEE Main

A round uniform body of radius $R$ , mass $M$ and moment of inertia $I$ , rolls down (without slipping) an inclined plane making an angle $θ$ with the horizontal. Then, its acceleration is

(A)

\frac{g s i n θ}{1 + I / M R ^{2}}

(B)

\frac{g s i n θ}{1 + M R ^{2} / I}

(C)

\frac{g s i n θ}{1 - I / M R ^{2}}

(D)

\frac{g s i n θ}{1 - M R ^{2} / I}

JEE Main 2021, 25 Feb Shift-II

LEVELJEE Main

A sphere of radius $a$ and mass $m$ rolls along a horizontal plane with constant speed $v_{0}$ . It encounters an inclined plane at angle $θ$ and climbs upwards. Assuming that it rolls without slipping, how far up the sphere will travel?

(A)

\frac{v _{0}^{2}}{2 g s i n θ}

(B)

\frac{v _{0}^{2}}{5 g s i n θ}

(C)

\frac{10 v _{0}^{2}}{7 g s i n θ}

(D)

\frac{2 v _{0}^{2}}{5 g s i n θ}

LEVELJEE Main

An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $F_{1} / F_{2}$ is

(A)

\frac{R _{2}}{R _{1}}

(B)

(\frac{R _{1}}{R _{2}})^{2}

(C)

(D)

\frac{R _{1}}{R _{2}}

JEE Advanced 1997

LEVELJEE Advanced

A uniform disc of mass $m$ and radius $R$ is rolling up a rough inclined plane which makes an angle of $3 0^{\circ}$ with the horizontal. If the coefficients of static and kinetic friction are each equal to $μ$ and the only forces acting are gravitational and frictional, then the magnitude of the frictional force acting on the disc is ……… and its direction is ……… (write up or down) the inclined plane.

JEE Advanced 2016

LEVELJEE Main

A roller is made by joining together two corners at their vertices $O$ . It is kept on two rails $A B$ and $C D$ which are placed asymmetrically (see the figure), with its axis perpendicular to $C D$ and its centre $O$ at the centre of line joining $A B$ and $C D$ (see the figure). It is given a light push, so that it starts rolling with its centre $O$ moving parallel to $C D$ in the direction shown. As it moves, the roller will tend to

turn left and right alternately

JEE Advanced 1997

LEVELJEE Advanced

Two thin circular discs of mass 2 kg and radius 10 cm each are joined by a rigid massless rod of length 20 cm. The axis of the rod is along the perpendicular to the planes of the disc through their centres. This object is kept on a truck in such a way that the axis of the object is horizontal and perpendicular to the direction of motion of the truck. Its friction with the floor of the truck is large enough, so that the object can roll on the truck without slipping. Take X-axis as the direction of motion of the truck and Z-axis as the vertically upwards direction. If the truck has an acceleration $9 m/s^{2}$ , calculate (a) the force of friction on each disc and (b) the magnitude and direction of the frictional torque acting on each disc about the centre of mass $O$ of the object. Express the torque in the vector form in terms of unit vectors $\hat{i}, \hat{j}$ and $\hat{k}$ in $x, y$ and $z$ -directions.

JEE Advanced 2002

LEVELJEE Main

A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are

(A)

up the incline while ascending and down the incline while descending

(B)

up the incline while ascending as well as descending

(C)

down the incline while ascending and up the incline while descending

(D)

down the incline while ascending as well as descending

JEE Advanced 2004

LEVELJEE Main

A disc is rolling (without slipping) on a horizontal surface. $C$ is its centre and $Q$ and $P$ are two points equidistant from $C$ . Let $v_{P}$ , $v_{Q}$ and $v_{C}$ be the magnitude of velocities of points $P$ , $Q$ and $C$ respectively, then

(A)

v_{Q} > v_{C} > v_{P}

(B)

v_{Q} < v_{C} < v_{P}

(C)

v_{Q} = v_{P}, v_{C} = \frac{1}{2} v_{P}

(D)

v_{Q} < v_{C} > v_{P}

JEE Advanced 2012

LEVELJEE Main

The figure shows a system consisting of (i) a ring of outer radius $3 R$ rolling clockwise without slipping on a horizontal surface with angular speed $ω$ and (ii) an inner disc of radius $2 R$ rotating anti-clockwise with angular speed $ω /2$ . The ring and disc are separated by frictionless ball bearings. The system is in the $x - z$ plane. The point $P$ on the inner disc is at a distance $R$ from the origin, where $O P$ makes an angle of $3 0^{\circ}$ with the horizontal. Then with respect to the horizontal surface,

* Multiple Correct Options

(A)

the point

O

has a linear velocity

3 R ω \hat{i}

(B)

the point

P

has a linear velocity

\frac{11}{4} R ω \hat{i} + \frac{3}{4} R ω \hat{k}

(C)

the point

P

has a linear velocity

\frac{13}{4} R ω \hat{i} - \frac{3}{4} R ω \hat{k}

(D)

the point

P

has a linear velocity

(3 - \frac{3}{4}) R ω \hat{i} + \frac{1}{4} R ω \hat{k}

JEE Advanced 2005

LEVELJEE Main

A solid cylinder rolls without slipping on an inclined plane inclined at an angle $θ$ . Find the linear acceleration of the cylinder. Mass of the cylinder is $M$ .

JEE Advanced 1988

LEVELJEE Advanced

A cylinder of mass $M$ and radius $R$ is resting on a horizontal platform (which is parallel to the $x$ - $y$ plane) with its axis fixed along the $Y$ -axis and free to rotate about its axis. The platform is given a motion in the $x$ -direction given by $x = A cos (ω t)$ . There is no slipping between the cylinder and platform. The maximum torque acting on the cylinder during its motion is ......... .

JEE Advanced 1999

LEVELJEE Advanced

A man pushes a cylinder of mass $m_{1}$ with the help of a plank of mass $m_{2}$ as shown. There is no slipping at any contact. The horizontal component of the force applied by the man is $F$ . Find (a) the accelerations of the plank and the centre of mass of the cylinder and (b) the magnitudes and directions of frictional forces at contact points.

JEE Advanced 2012

LEVELJEE Main

Two solid cylinders $P$ and $Q$ of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder $P$ has most of its mass concentrated near its surface, while $Q$ has most of its mass concentrated near the axis. Which statement(s) is(are) correct?

(A)

Both cylinders

P

and

Q

reach the ground at the same time

(B)

Cylinder

P

has larger linear acceleration than cylinder

Q

(C)

Both cylinders reach the ground with same translational kinetic energy

(D)

Cylinder

Q

reaches the ground with larger angular speed

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is

A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A solid cylinder rolls without slipping on an inclined plane inclined at an angle θ. Find the linear acceleration of the cylinder. Mass of the cylinder is M.

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is $50%$ of its translational kinetic energy. The body is

A uniform sphere of mass $500 g$ rolls without slipping on a plane horizontal surface with its centre moving at a speed of $5.00 cm/s$ . Its kinetic energy is

A solid cylinder rolls without slipping on an inclined plane inclined at an angle $θ$ . Find the linear acceleration of the cylinder. Mass of the cylinder is $M$ .