Question

A $5kg$ body is rotated in a vertical circle with a constant speed of $4m{s}^{-1}$ using a string of length $1m$, when the tension in the string is $31N$, then the body will be:

• A. At the lowest point
• B. Making an angle ${30}^o$ with vertical
• C. At the highest point
• D. At horizontal position

Answer 1

The correct option is C At the highest point

Given,

$m\left(Mass\right)=5kg,r\left(radius\right)=1mandv\left(velocity\right)=4m{s}^{-1}$

Let, $\theta \left(angle\right)madewithverticalaxis$

Centripetal force, $F_c=\frac{m{v}^2}{r}=\frac{5\times 4^2}{1}=80N$

weight, $W=mg\cos \theta =5\times 9.8\cos \theta =49\cos \theta$

Tension in the string, $T$

$T=F_r+W$

$31=80+49\cos \theta$

$\cos \theta =\frac{31-80}{49}=-1$

$\theta =\cos (-1)={180}^o$

Hence, body at the highest point.