A solid sphere rolls without slipping, first horizontally and then up to a point X at height h on an inclined plane before rolling down, as shown in the figure below. The initial horizontal speed of the sphere is

Question

A solid sphere rolls without slipping, first horizontally and then up to a point X at height h on an inclined plane before rolling down, as shown in the figure below. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/a114857c980508729c0007c1703385fc-.jpeg" /> The initial horizontal speed of the sphere is (A) √7gh /5 (B) √5gh /7 (C) √2gh  (D) √10gh /7

Tardigrade Admin · Accepted Answer

Let initial horizontal speed of sphere is

υ

. Then, total kinetic energy of sphere on horizontal part

= (K E)_{translation} + (K E)_{rotation}

= \frac{1}{2} m υ^{2} + \frac{1}{2} I ω^{2}

= \frac{1}{2} m υ^{2} + \frac{1}{2} \times \frac{2}{5} m R^{2} \times \frac{υ ^{2}}{R ^{2}} = \frac{7}{10} m υ^{2}

If sphere rises upto height

h

then, by conservation of energy, we have
mgh

= \frac{7}{10} m υ^{2}

or

υ = \frac{10}{7} g h

Q. A solid sphere rolls without slipping, first horizontally and then up to a point $X$ at height h on an inclined plane before rolling down, as shown in the figure below.

The initial horizontal speed of the sphere is

$7 g h /5$

$5 g h /7$

$2 g h$

$10 g h /7$

Q. A solid sphere rolls without slipping, first horizontally and then up to a point X at height h on an inclined plane before rolling down, as shown in the figure below. The initial horizontal speed of the sphere is

7gh/5​

5gh/7​

2gh​

10gh/7​

Q. A solid sphere rolls without slipping, first horizontally and then up to a point $X$ at height h on an inclined plane before rolling down, as shown in the figure below.

The initial horizontal speed of the sphere is

$7 g h /5$

$5 g h /7$

$2 g h$

$10 g h /7$