A hollow sphere of mass m starting from rest rolls down- without slipping- on an inclined plane of inclination - What is the total energy of the sphere after 10-5s if velocity after 10-5s is v-

The correct option is A 5/6mv^2 Total K.E, #160; #160; E= 12mv^2 + 12 I #160; #160;w^2 E= 12mv^2 + 12×23mR^2 #160; #160;w^2 ...

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Byju's Answer

Standard XII

Physics

Direction of Friction

A hollow sphe...

Question

A hollow sphere of mass $m$ starting from rest rolls down, without slipping, on an inclined plane of inclination $θ$ . What is the total energy of the sphere after $10^{- 5} s$ if velocity after $10^{- 5} s$ is $v$ ?

5 / 6 m v^{2}

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2 / 3 m v^{2}

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10^{- 5} m v^{2}

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m v^{2} / 10^{- 5}

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Solution

The correct option is A $5 / 6 m v^{2}$
Total K.E, $E = \frac{1}{2} m v^{2} + \frac{1}{2} I w^{2}$
$E = \frac{1}{2} m v^{2} + \frac{1}{2} \times \frac{2}{3} m R^{2} w^{2}$
$E = \frac{1}{2} m v^{2} + \frac{1}{2} \times \frac{2}{3} m v^{2}$ (as $v = R w$ no slipping)
$E = \frac{5}{6} m v^{2}$

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A hollow sphere of mass m starting from rest rolls down, without slipping, on an inclined plane of inclination θ. What is the total energy of the sphere after 10−5s if velocity after 10−5s is v?

The correct option is A 5/6mv2Total K.E, E=12mv2+12Iw2E=12mv2+12×23mR2w2E=12mv2+12×23mv2 (as v=Rw no slipping)E=56mv2

A hollow sphere of mass $m$ starting from rest rolls down, without slipping, on an inclined plane of inclination $θ$ . What is the total energy of the sphere after $10^{- 5} s$ if velocity after $10^{- 5} s$ is $v$ ?

The correct option is A $5 / 6 m v^{2}$
Total K.E, $E = \frac{1}{2} m v^{2} + \frac{1}{2} I w^{2}$
$E = \frac{1}{2} m v^{2} + \frac{1}{2} \times \frac{2}{3} m R^{2} w^{2}$
$E = \frac{1}{2} m v^{2} + \frac{1}{2} \times \frac{2}{3} m v^{2}$ (as $v = R w$ no slipping)
$E = \frac{5}{6} m v^{2}$