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:

Question

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: (A) (F/3 m R) (B) (3 F/2 m R) (C) (2 F/3 m R) (D) (F/2 m R)

Tardigrade Admin · Accepted Answer

F-fr=ma ldots (i) frR=Iα =(m R2/2)α ldots (.ii.) For pure rolling a=α R ldots (.iii.) From (i), (.ii.) and (.iii.) F-(m R α /2)=mα R F=(3/2)mR α α =(2 F/3 m R)

Q. 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:

$\frac{F}{3 m R}$

$\frac{3 F}{2 m R}$

$\frac{2 F}{3 m R}$

$\frac{F}{2 m R}$

$F - f_{r} = ma$ $\dots (i)$
$f_{r} R = I α = \frac{m R ^{2}}{2} α$ $\dots (ii)$
For pure rolling
$a = α R$ $\dots (iii)$
From $(i), (ii)$ and $(iii)$
$F - \frac{m R α}{2} = m α R$
$F = \frac{3}{2} m R α$
$α = \frac{2 F}{3 m R}$

Q. 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:

3mRF​

2mR3F​

3mR2F​

2mRF​