When a uniform solid sphere and a disc of the | vedclass

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

Question

(C) The linear acceleration $a$ of a body rolling down an inclined plane is given by $a = \frac{g \sin 	heta}{1 + \frac{K^2}{R^2}}$,where $K$ is the

Vedclass · Accepted Answer

$\sqrt{14} : \sqrt{15}$

Vedclass · Answer

(C) The linear acceleration $a$ of a body rolling down an inclined plane is given by $a = \frac{g \sin 	heta}{1 + \frac{K^2}{R^2}}$,where $K$ is the radius of gyration.For a solid sphere,$K^2 = \frac{2}{5}R^2$,so $a_s = \frac{g \sin 	heta}{1 + 2/5} = \frac{5}{7} g \sin 	heta$.For a disc,$K^2 = \frac{1}{2}R^2$,so $a_d = \frac{g \sin 	heta}{1 + 1/2} = \frac{2}{3} g \sin 	heta$.Since the distance $s$ is the same and they start from rest,$s = \frac{1}{2} a t^2$,which implies $t = \sqrt{\frac{2s}{a}}$.Therefore,the ratio of times is $\frac{t_s}{t_d} = \sqrt{\frac{a_d}{a_s}} = \sqrt{\frac{(2/3) g \sin 	heta}{(5/7) g \sin 	heta}} = \sqrt{\frac{2}{3} 	imes \frac{7}{5}} = \sqrt{\frac{14}{15}}$.Thus,the ratio is $\sqrt{14} : \sqrt{15}$.

When a uniform solid sphere and a disc of the same mass and of the same radius roll down a rough inclined plane from rest to the same distance,then the ratio of the time taken by them is

Similar Questions

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 . . . . . . .

$A$ 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 $h$. Choose the correct statement$(s)$ related to the motion of each body.

$A$ body rolls down an inclined plane without slipping. The kinetic energy of rotation is $50 \%$ of its translational kinetic energy. The body is :

$A$ ring takes times $t_1$ and $t_2$ to reach the bottom of an inclined plane of length $L$ by sliding and rolling,respectively. What is the ratio of $t_1$ to $t_2$?

$A$ solid sphere of mass $M$ and radius $R$ is rolling down an inclined plane of length $L$ and height $h$ without slipping. What will be the velocity of its center of mass upon reaching the bottom?

Vedclass Test Series

Exam Paper Generator

Online Exam Module