Motion in a Plane - Result Question 56
59. A ball of mass $0.25 kg$ attached to the end of a string of length $1.96 m$ is moving in a horizontal circle. The string will break if the tension is more than $25 N$. What is the maximum speed with which the ball can be moved?
[1998]
(a) $14 m / s$
(b) $3 m / s$
(c) $5 m / s$
(d) $3.92 m / s$
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Answer:
Correct Answer: 59. (a)
Solution:
(a) $T=\frac{m v^{2}}{R}$
$v=\sqrt{\frac{T R}{m}}=\sqrt{\frac{25 \times 1.96}{0.25}}$
$=\frac{5 \times 14}{5}=14 m / s$
In the horizontal circular motion of the ball tension in the string is balanced by the centrifugal force $(\frac{m v^{2}}{\ell})$ and hence the maximum tension in the string will be for the maximum speed of the ball.
