First slide

Circular motion in horizontal plane

Question

A string of length L is fixed at one end and carries a mass M at the other end. The string makes $\frac{2}{π}$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is

Moderate

A

ML
B

2 ML
C

4 ML
D

16 ML

Solution

T $\sin θ = {Mω}^{2} R$ -------------------(i)
$T \sin θ = {Mω}^{2} L \sin θ$ ----------(ii)
From (i) and (ii)
$T = {Mω}^{2} L$
= $M 4 π^{2} n^{2} L$
= $M 4 π^{2} {(\frac{2}{π})}^{2} L$
= 16 ML

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