Question

A mass of 0.1 kg is rotated in a vertical circle using a string of length 20 cm. When the string makes an angle of ${30}^0$ with the vertical, the speed of the mass is $1.5m{s}^{-1}$ . The tangential acceleration of the mass at that instant is:

• A. $13.0N$
• B. $42N$
• C. $45N$
• D. $50N$

Answer 1

The correct option is A $13.0N$

This problem is an example of circular motion$,$ so the equation to use will be$:$

F = (mv²) / r

where F is the centripetal force (acting towards the centre of the circle$),$ m is mass$,v$ is velocity and r is radius

Therefore we can calculate what the centripetal force will be$:$

$F=14.94222N$

As we said earlier$,$ there are two forces acting on the mass towards the centre of the circle$:$ its weight and the tension$.$

We can calculate the weight from the body's mass using $W=m\times g$

$W=0.2\times 9.81$

Then$,F=weight+tension$

tension $=F-weight$

tension $=14.942-0.2\times 9.81$

tension$=13.0N$

Hence,

option $\left(A\right)$ is correct answer.