A solid sphere is rotating about a diameter at an angular velocity ω . If it coots so that its radius reduces to (1/n) of its original value, its angular velocity becomes

Question

A solid sphere is rotating about a diameter at an angular velocity ω . If it coots so that its radius reduces to (1/n) of its original value, its angular velocity becomes (A)  (ω /n)  (B)  (ω /n2)  (C)  nω  (D)  n2ω

Tardigrade Admin · Accepted Answer

From law of conservation of angular momentum, if no external torque is acting upon a body rotating about an axis, then the angular momentum of the body remains constant that is

J = I ω

Also,

I = \frac{2}{5} M R^{2}

for a solid sphere.
Given,

R_{1} = R, R_{2} = \frac{R}{n}

∴ \frac{2}{5} M R^{2} ω_{1} = \frac{2}{5} M (\frac{R}{n})^{2} \times ω_{2}

\Rightarrow ω_{2} = n^{2} ω_{1}

= m^{2} ω

Q. A solid sphere is rotating about a diameter at an angular velocity $ω .$ If it coots so that its radius reduces to $\frac{1}{n}$ of its original value, its angular velocity becomes

$\frac{ω}{n}$

$\frac{ω}{n ^{2}}$

$nω$

$n^{2} ω$

Q. A solid sphere is rotating about a diameter at an angular velocity ω. If it coots so that its radius reduces to n1​ of its original value, its angular velocity becomes

nω​

n2ω​

nω

n2ω

Q. A solid sphere is rotating about a diameter at an angular velocity $ω .$ If it coots so that its radius reduces to $\frac{1}{n}$ of its original value, its angular velocity becomes

$\frac{ω}{n}$

$\frac{ω}{n ^{2}}$

$nω$

$n^{2} ω$