A hollow sphere of mass M and radius R is released from height h on a inclined plane. If hollow sphere is rolling without slipping on the inclined then velocity of centre of sphere when it reaches the bottom of inclined plane is

Question

A hollow sphere of mass M and radius R is released from height h on a inclined plane. If hollow sphere is rolling without slipping on the inclined then velocity of centre of sphere when it reaches the bottom of inclined plane is (A) √2 gh (B) √(6 gh/5) (C) √(3 gh/5) (D) √(2 gh/5)

Tardigrade Admin · Accepted Answer

M.Ei = MEf mgh= (1/2)Icomω2+ (1/2)mv2 mgh = (1/2)× m R2× (2/3)× (V2/R2)+(1/2)mv2 mgh = (5/6)mv2⇒ v = √(6 gh/5)

Q. A hollow sphere of mass M and radius R is released from height h on a inclined plane. If hollow sphere is rolling without slipping on the inclined then velocity of centre of sphere when it reaches the bottom of inclined plane is

$2 g h$

$\frac{6 g h}{5}$

$\frac{3 g h}{5}$

$\frac{2 g h}{5}$

$M . E_{i} = M E_{f}$
$m g h = \frac{1}{2} I_{co m} ω^{2} + \frac{1}{2} m v^{2}$
$m g h = \frac{1}{2} \times m R^{2} \times \frac{2}{3} \times \frac{V ^{2}}{R ^{2}} + \frac{1}{2} m v^{2}$
$m g h = \frac{5}{6} m v^{2} \Rightarrow v =$ $\frac{6 g h}{5}$

Q. A hollow sphere of mass M and radius R is released from height h on a inclined plane. If hollow sphere is rolling without slipping on the inclined then velocity of centre of sphere when it reaches the bottom of inclined plane is

2gh​

56gh​​

53gh​​

52gh​​

M.Ei​=MEf​ mgh=21​Icom​ω2+21​mv2 mgh=21​×mR2×32​×R2V2​+21​mv2 mgh=65​mv2⇒v= 56gh​​

$2 g h$

$\frac{6 g h}{5}$

$\frac{3 g h}{5}$

$\frac{2 g h}{5}$

$M . E_{i} = M E_{f}$
$m g h = \frac{1}{2} I_{co m} ω^{2} + \frac{1}{2} m v^{2}$
$m g h = \frac{1}{2} \times m R^{2} \times \frac{2}{3} \times \frac{V ^{2}}{R ^{2}} + \frac{1}{2} m v^{2}$
$m g h = \frac{5}{6} m v^{2} \Rightarrow v =$ $\frac{6 g h}{5}$