Question

2. The radius of a rotating sphere decreases by 2%
keeping the mass constant, the change in its
rotational kinetic energy ?
(1) 2% (2) 1% (3) 4% (4) 8%
171
.111​

Answer 1

$\huge\underline\blue{\rm Answer:}$

$\red{\boxed{\sf Change\:in\: Rotational\: Kinetic\:energy=4percent}}$

$\huge\underline\blue{\rm Solution:}$

$\large\underline\pink{\sf Given: }$

• Radius of a rotating sphere decreases ($\sf{\frac{\delta R}{R}}$)= 2%

$\large\underline\pink{\sf To\:Find: }$

• Change in its
• rotational kinetic energy $\sf{\frac{\delta K_{rotation}}{K_{rotation}}}$=?

━━━━━━━━━━━━━━━━━━━━━━━━━━

We know ,

$\Large{\boxed{\sf K_{rotational}=\frac12I\omega^2}}$

$\large\implies{\sf \frac12×25×mR^2\omega^2}$

$\Large{\boxed{\sf \frac{\delta K_{Rotational}}{K_{Rotational}}=2\frac{\delta R}{R}}}$

$\large\implies{\sf 2×2 percent}$

$\large\implies{\sf 4 percent }$

$\red{\boxed{\sf Change\:in\: Rotational\: Kinetic\:energy=4percent}}$