A solid cylinder P rolls without slipping fro | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For cylinder $P$ (rolling without slipping):By the principle of conservation of energy,the initial potential energy is converted into translationa

Vedclass · Accepted Answer

$\sqrt{\frac{3}{2}}$

Vedclass · Answer

(B) For cylinder $P$ (rolling without slipping):By the principle of conservation of energy,the initial potential energy is converted into translational and rotational kinetic energy at the bottom:$mgh = \frac{1}{2}mv_p^2 + \frac{1}{2}I\omega^2$Since $I = \frac{1}{2}mr^2$ and $v_p = r\omega$,we have:$mgh = \frac{1}{2}mv_p^2 + \frac{1}{2}(\frac{1}{2}mr^2)(\frac{v_p}{r})^2$$mgh = \frac{1}{2}mv_p^2 + \frac{1}{4}mv_p^2 = \frac{3}{4}mv_p^2$$v_p = \sqrt{\frac{4gh}{3}}$For cylinder $Q$ (sliding without friction):Since there is no friction,the cylinder does not rotate. All potential energy is converted into translational kinetic energy:$mgh = \frac{1}{2}mv_q^2$$v_q = \sqrt{2gh}$The ratio of the speeds is:$\frac{v_q}{v_p} = \frac{\sqrt{2gh}}{\sqrt{\frac{4gh}{3}}} = \sqrt{2 \cdot \frac{3}{4}} = \sqrt{\frac{3}{2}}$

Similar Questions

$A$ ring is rolling on an inclined plane. The ratio of the linear and rotational kinetic energies will be

$A$ body is rolling down an inclined plane. If the kinetic energy of rotation is $40\%$ of the translational kinetic energy,then the body is a

An object of uniform density rolls up a curved path with an initial velocity $v_0$ as shown in the figure. If the maximum height attained by the object is $\frac{7v_0^2}{10g}$ ($g =$ acceleration due to gravity), the object is a . . . . . . .

$A$ sphere,a disc,a ring,and a hollow sphere of the same radius are rolled down from the same height on an inclined plane simultaneously. The order in which these objects reach the bottom is:

$A$ body slides down a smooth inclined plane of inclination $\theta$ and reaches the bottom with velocity $V$. If the same body is a ring which rolls down the same inclined plane,then the linear velocity at the bottom of the plane is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module