(A) The velocity $v$ of a body rolling down an inclined plane of height $h$ is given by the formula:$v = \sqrt{\frac{2gh}{1 + \frac{K^2}{R^2}}}$Here,$

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$\sqrt{\frac{4gL\sin\theta}{3}}$

(A) The velocity $v$ of a body rolling down an inclined plane of height $h$ is given by the formula:$v = \sqrt{\frac{2gh}{1 + \frac{K^2}{R^2}}}$Here,$h = L \sin\theta$ and for a disc,the radius of gyration $K$ is given by $K^2 = \frac{R^2}{2}$,so $\frac{K^2}{R^2} = \frac{1}{2}$.Substituting these values into the formula:$v = \sqrt{\frac{2g(L \sin\theta)}{1 + \frac{1}{2}}}$$v = \sqrt{\frac{2gL \sin\theta}{\frac{3}{2}}}$$v = \sqrt{\frac{4gL \sin\theta}{3}}$

Class 11 Physics System of Particles and Rotational Motion Rolling On Inclined Plane

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$A$ disc rolls without slipping down an inclined plane of length $L$ and inclination $\theta$. What will be its velocity at the bottom?

A
$\sqrt{\frac{4gL\sin\theta}{3}}$
B
$\sqrt{\frac{2gL\sin\theta}{3}}$
C
$\sqrt{\frac{10gL\sin\theta}{7}}$
D
$\sqrt{4gL\sin\theta}$

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System of Particles and Rotational Motion

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Rolling On Inclined Plane

Two identical solid cylinders run a race starting from rest at the top of an inclined plane. If one cylinder slides and the other rolls,which of the following statements is true?

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$A$ solid cylinder and a hollow cylinder,both of the same mass and same external diameter,are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

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$A$ solid cylinder $(i)$ rolls down and $(ii)$ slides down an inclined plane. What is the ratio of the accelerations in these conditions?

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$A$ cylinder and a ring of same mass $M$ and radius $R$ are placed on the top of a rough inclined plane of inclination $\theta$. Both are released simultaneously from the same height $h$. When these bodies roll down to the foot of the inclined plane,then

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Derive expressions for the kinetic energy and velocity of a body rolling without sliding down an inclined plane of inclination $\theta$.

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$A$ disc rolls without slipping down an inclined plane of length $L$ and inclination $\theta$. What will be its velocity at the bottom?

Similar Questions

Two identical solid cylinders run a race starting from rest at the top of an inclined plane. If one cylinder slides and the other rolls,which of the following statements is true?

$A$ solid cylinder and a hollow cylinder,both of the same mass and same external diameter,are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

$A$ solid cylinder $(i)$ rolls down and $(ii)$ slides down an inclined plane. What is the ratio of the accelerations in these conditions?

$A$ cylinder and a ring of same mass $M$ and radius $R$ are placed on the top of a rough inclined plane of inclination $\theta$. Both are released simultaneously from the same height $h$. When these bodies roll down to the foot of the inclined plane,then

Derive expressions for the kinetic energy and velocity of a body rolling without sliding down an inclined plane of inclination $\theta$.

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