A spherical shell and a solid cylinder of same radius rolls down an inclined plane. The ratio of their accelerations will be:-

Question

A spherical shell and a solid cylinder of same radius rolls down an inclined plane. The ratio of their accelerations will be:- (A) 15:14 (B) 9:10 (C) 2:3 (D) 3:5

Tardigrade Admin · Accepted Answer

Acceleration of a purely rolling object on an inclined plane is :-

a = \frac{g s in θ}{( 1 + \frac{K ^{2}}{R ^{2}} )}

for spherical shell,

\frac{K ^{2}}{R ^{2}} = \frac{2}{3}

for solid cylinder,

\frac{K ^{2}}{R ^{2}} = \frac{1}{2}

so,

\frac{a _{shell}}{a _{cylinder}} = \frac{\frac{g s in θ}{( 1 + \frac{2}{3} )}}{\frac{g s in θ}{( 1 + \frac{1}{2} )}} = \frac{9}{10}

Q. A spherical shell and a solid cylinder of same radius rolls down an inclined plane. The ratio of their accelerations will be:-

$15 : 14$

$9 : 10$

$2 : 3$

$3 : 5$

Q. A spherical shell and a solid cylinder of same radius rolls down an inclined plane. The ratio of their accelerations will be:-

15:14

9:10

2:3

3:5

Acceleration of a purely rolling object on an inclined plane is :- a=(1+R2K2​)gsinθ​ for spherical shell, R2K2​=32​ for solid cylinder, R2K2​=21​ so, acylinder ​ashell ​​=(1+21​)gsinθ​(1+32​)gsinθ​​=109​

$15 : 14$

$9 : 10$

$2 : 3$

$3 : 5$