Question

An object of mass 0.5 kg attached to a string of length 0.5m is whirled in a vertical circle with constant angular speed. If maximum tension in the string is 5 kg wt calculate 1) speed of object 2) maximum number of revolutions per min

Answer 1

Answer:

The speed is 4.95 m/s and the maximum number of revolutions per min is 94.59 rpm.

Explanation:

Given that,

Mass of the object = 0.5 kg

Length l = 0.5 m

Tension T = 5 kg wt

(1). Using formula of maximum tension

The speed of object is

$v = \sqrt{5gr}$

$v = \sqrt{5\times9.8\times0.5}$

$v=4.95\ m/s$

(2). The maximum number of revolutions per min

Using formula of angular velocity

$v = r\omega$

$4.95=0.5\times\omega$

$\omega=\dfrac{4.95}{0.5}$

$\omega= 9.9\ rad/s$

The maximum number of revolutions per min

$\omega = 9.9\times\dfrac{60}{2\pi}$

$\omega = 9.9\times\dfrac{60}{2\times3.14}$

$\omega=94.59\ rpm$

Hence, The speed is 4.95 m/s and the maximum number of revolutions per min is 94.59 rpm.