A ball of mass 0.12 kg is being whirled in a horizontal circle at the end of string 0.5 m long. It is capable of making 231 revolutions in one minute. The breaking tension of the string is

Question

A ball of mass 0.12 kg is being whirled in a horizontal circle at the end of string 0.5 m long. It is capable of making 231 revolutions in one minute. The breaking tension of the string is (A) 3 N (B) 15.1 N (C) 31.5 N (D) 35.1 N

Tardigrade Admin · Accepted Answer

When body preforms circular motion, it is acted upon by a centripetal force the magnitude of which is given by
where, m is mass, v the velocity and r the radius.
since

ν = r ω

=

F = m r ω^{2}

Given, m = 0.1 kg, r = 0.5 m,

ω

= 231 rpm =

\frac{2 π \times 231}{60} r a d s^{- 1}

= 24.2 rad/s
F =

0.12 \times 0.5 \times (24.2)^{2}

= 35.1 N

Q. A ball of mass 0.12 kg is being whirled in a horizontal circle at the end of string 0.5 m long. It is capable of making 231 revolutions in one minute. The breaking tension of the string is

3 N

15.1 N

31.5 N

35.1 N

When body preforms circular motion, it is acted upon by a centripetal force the magnitude of which is given by where, m is mass, v the velocity and r the radius. since ν=rω = F=mrω2 Given, m = 0.1 kg, r = 0.5 m, ω = 231 rpm = 602π×231​rads−1 = 24.2 rad/s F = 0.12×0.5×(24.2)2 = 35.1 N