A 5 kg mass is rotating on a circular path of radius 1 m with angular velocity of 50 rad / sec. If radius of path becomes 5 m. The value of angular velocity will be

Question

A 5 kg mass is rotating on a circular path of radius 1 m with angular velocity of 50 rad / sec. If radius of path becomes 5 m. The value of angular velocity will be (A) 7 rad / s (B) 3 rad / s (C) 4 rad / s (D) 2 rad / s

Tardigrade Admin · Accepted Answer

Angular momentum L=m v r=m ω r × r=m ω r2 ∴ (ω2/ω1)=((r1/r2))2 ⇒ ω2=((1/5))2 × 50 =(50/25)=2 rad / s

Q. A $5 k g$ mass is rotating on a circular path of radius $1 m$ with angular velocity of $50 r a d / sec$ . If radius of path becomes $5 m$ . The value of angular velocity will be

$7 r a d / s$

$3 r a d / s$

$4 r a d / s$

$2 r a d / s$

Angular momentum $L = m v r = mω r \times r = mω r^{2}$
$∴ \frac{ω _{2}}{ω _{1}} = (\frac{r _{1}}{r _{2}})^{2}$
$\Rightarrow ω_{2} = (\frac{1}{5})^{2} \times 50$
$= \frac{50}{25} = 2 r a d / s$

Q. A 5kg mass is rotating on a circular path of radius 1m with angular velocity of 50rad/sec. If radius of path becomes 5m. The value of angular velocity will be

7rad/s

3rad/s

4rad/s

2rad/s