SATHEE: Rotational Motion Question 221

Rotational Motion Question 221

Question: The spherical body and block is m. Moment of inertia of the spherical body about centre of mass is $2 m R^{2}$ . The spherical body rolls on the horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is

Options:

A) 3/4

B) 1/3

C) 2/3

D) 1/2

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Let v be the linear velocity of centre of mass of the spherical body and w its angular velocity about centre of mass.

Then $ω = \frac{v}{2 R}$

KE of spherical body

$K_{1} = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$

$K_{1} = \frac{1}{2} m v^{2} + \frac{1}{2} {(2 m R)}^{2} (\frac{v^{2}}{4 R^{2}}) = \frac{3}{4} m v^{2}$ ?.

(i) Speed of the block will be

$v^{'} = (ω) (3 R) = 3 R ω = (3 R) (\frac{v}{2 R}) = \frac{3}{2} v$

$∴$ KE of block $K_{2} = \frac{1}{2} m v^{2}$

$= \frac{1}{2} m {(\frac{3}{2} v)}^{2} = \frac{9}{8} m v^{2}$

From equations (i) and (ii), $

$\frac{K_{1}}{K_{2}} = \frac{2}{3}$

Rotational Motion Question 221

Question: The spherical body and block is m. Moment of inertia of the spherical body about centre of mass is $2 m R^{2}$ . The spherical body rolls on the horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is

Options:

Answer:

Solution:

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Rotational Motion Question 221

Question: The spherical body and block is m. Moment of inertia of the spherical body about centre of mass is 2mR2 . The spherical body rolls on the horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: The spherical body and block is m. Moment of inertia of the spherical body about centre of mass is $2 m R^{2}$ . The spherical body rolls on the horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is