Question

The maximum mass that can be hung vertically
from a string without breaking the string is 10 kg.
A length of this string that is 2 m long is used to
rotate a 0.5 kg object in a circle on a frictionless
table with the string horizontal. The maximum
speed that the mass can attain under these
conditions without the string breaking is most
nearly

Answer 1

Given :-

Mass = m = 10 Kg

Acceleration due to gravity = g = 10 ms-²

Length of string = r = 2 m

From this given data we can find the maximum force that the string can tolerate.

F = mg

F = 10 × 10

$\bf{{F}_{max}\:=\:100\:N}$

Here, as the body moves in a circular loop there will be centripetal force acting on it and the mass is 0.5 Kg.

We can find Centripetal acceleration using this mass.

a = F/m'

a = 100/0.5

$\bf{{a}_{c}\:=\:200\:m{s}^{-2}}$

Again using, the formula we can find the velocity.

a = v²/r

200 × 2 = v²

v = √400

$\bf{{v}_{max}\:=\:20\:m{s}^{-1}}$