A ball of mass 0.25 kg attached to the ends of a string of length 1.96 m is rotating in a horizontal circle. The string will break, if tension is more than 25 N. What is the maximum velocity with which the ball can be rotated?

Question

A ball of mass 0.25 kg attached to the ends of a string of length 1.96 m is rotating in a horizontal circle. The string will break, if tension is more than 25 N. What is the maximum velocity with which the ball can be rotated? (A) 3 m/s (B) 5 m/s (C) 9 m/s (D) 14 m/s

Tardigrade Admin · Accepted Answer

Given: m=0.25 kg , l=1.96 m and t=25 N Centrifugal force (tension) in the string is given by F=(m v2/r) ⇒ v2=(F r/m) ⇒ v2=(25 × 1.96/0.25)=196 ⇒ v=√196=14 m / s

Q. A ball of mass $0.25 k g$ attached to the ends of a string of length $1.96 m$ is rotating in a horizontal circle. The string will break, if tension is more than $25 N$ . What is the maximum velocity with which the ball can be rotated?

3 m/s

5 m/s

9 m/s

14 m/s

Given: $m = 0.25 k g, l = 1.96 m$
and $t = 25 N$
Centrifugal force (tension) in the string is given by
$F = \frac{m v ^{2}}{r}$
$\Rightarrow v^{2} = \frac{F r}{m}$
$\Rightarrow v^{2} = \frac{25 \times 1.96}{0.25} = 196$
$\Rightarrow v = 196 = 14 m / s$

Q. A ball of mass 0.25kg attached to the ends of a string of length 1.96m is rotating in a horizontal circle. The string will break, if tension is more than 25N. What is the maximum velocity with which the ball can be rotated?