Question

A body of mass $1kg$ tied to one end of string is revolved in a horizontal circle of radius $0.1m$ with a speed of $3evolution/sec$, assuming the effect of gravity is negligible, then linear velocity, acceleration and tension in the string be :

• A. $1.88m/s,35.5m/s^2,35.5N$
• B. $2.88m/s,45.5m/s^2,45.5N$
• C. $3.88m/s,55.5m/s^2,55.5N$
• D. None

Answer 1

The correct option is A $1.88m/s,35.5m/s^2,35.5N$

$3rev/sec⟹3\times 2\pi rad/sec$

or $\omega =6\pi radian/sec$

$v=r\omega =0.1\times 6\pi$

$=1.88m/s$

$T=m{\omega }^{2}r=1\times 36\times {\pi }^2\times 0.1$

$=35.5N$

$a_t=\alpha r$ and $a=0$ $\therefore a_t=0$

$a_c={\omega }^{2}r$ $=36\times {\pi }^2\times 0.1$ $a_c=35.5N$