Question

On horizontal smooth surface a mass of 2 kg is whirled
in a horizontal circle by means of a string at an initial
angular speed of 5 revolutions per minute. Keeping the
radius constant the tension in the string is doubled.
The new angular speed is nearly :
(A) 14 rpm (B) 10 rpm (C)2.25 rpm (D) 7 rpm​

Answer 1

Answer:

10

Explanation:

because it may double

Answer 2

$\LARGE\underline{\underline{\sf Given:}}$

• Mass = 2kg

• Angular Speed $\sf{(\omega_1)}$ = 5rpm

• Radius = constant = r

$\LARGE\underline{\underline{\sf To\:Find:}}$

• New Angular Speed $\sf{(\omega_2)}$ = ?

$\LARGE\underline{\underline{\sf Solution:}}$

T = m$\sf{a_c}$

Here ,

$\sf{a_c}$ = centripetal acceleration

$\implies{\sf T=m\omega_1^2r→(1) }$

Now ,

Tension is doubled ,

keeping radius constant

T' = 2T

T' = m$\sf{\omega_2^2}$r

2T = m$\sf{\omega_2^2r→(2)}$

From (1) and (2)

$\implies{\sf 2=\dfrac{\omega_2^2}{\omega_1^2}}$

$\implies{\sf \omega_2^2=2×\omega_1^2 }$

$\implies{\sf \omega_2^2=2×25 }$

$\implies{\sf \omega_2≈7\:rpm }$

$\LARGE\underline{\underline{\sf Answer:}}$

•°• New angular speed is nearly 7 rpm