A solid sphere is placed on a horizontal plane. A horizontal impulse l is applied at a distance h above the central line as shown in the figure. Soon after giving the impulse, the sphere starts rolling. The ratio (h/R) would be

Question

A solid sphere is placed on a horizontal plane. A horizontal impulse l is applied at a distance h above the central line as shown in the figure. Soon after giving the impulse, the sphere starts rolling. The ratio (h/R) would be <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-lvfsf7oszlllgfcx.jpg" /> (A) (1/2) (B) (2/5) (C) (1/4) (D) (1/5)

Tardigrade Admin · Accepted Answer

Assume the sphere is rotating with angular velocity

ω

and moving forward with velocity

v

. As the sphere is rolling without slipping,

v = ω R

Now change in linear momentum is due to Impulse

I

, so

I = m v

Also Angular momentum of the system is conserved, so about C

\Rightarrow I h = I_{0} ω

, here

I_{0}

is moment of inertia about the center of the sphere.

\Rightarrow m v h = \frac{2}{5} m R^{2} ω = \frac{2}{5} m R^{2} \frac{v}{R}

\Rightarrow \frac{h}{R} = \frac{2}{5}

Q. A solid sphere is placed on a horizontal plane. A horizontal impulse $l$ is applied at a distance $h$ above the central line as shown in the figure. Soon after giving the impulse, the sphere starts rolling. The ratio $\frac{h}{R}$ would be

$\frac{1}{2}$

$\frac{2}{5}$

$\frac{1}{4}$

$\frac{1}{5}$

Q. A solid sphere is placed on a horizontal plane. A horizontal impulse l is applied at a distance h above the central line as shown in the figure. Soon after giving the impulse, the sphere starts rolling. The ratio Rh​ would be

21​

52​

41​

51​

Q. A solid sphere is placed on a horizontal plane. A horizontal impulse $l$ is applied at a distance $h$ above the central line as shown in the figure. Soon after giving the impulse, the sphere starts rolling. The ratio $\frac{h}{R}$ would be

$\frac{1}{2}$

$\frac{2}{5}$

$\frac{1}{4}$

$\frac{1}{5}$