Question

A mass of 3 kg is whirled in a horizontal circle by
means of a string with initial speed of 6 r.p.m.
Keeping the radius constant the tension in the string
becomes 4 times. Then the new speed will be :-​

Answer 1

Answer:

The new speed will be 12rpm

Explanation:

solving on ground frame

Apply Newton's second law on mass(m) along centripetal direction (considering direction towards centre as positive)

∑$f_{c}$ = $ma_{c}$

T = mr$w_{2}$

For initial condition FBD

T = mr$w_{}^{2}$  ....(1)

from final condition FBD

4T = mr$w_{2}^{2}$

$w_{2}^{2}$= $\frac{4T}{mr}$    ....(2)

substituting value of T in eq(2)

$w_{2}^{2}$ = $\frac{4mrw^{2} }{mr}$

$w_{2}$ = $\sqrt{4w^{2} }$

$w_{2}$ = 2$w_{}$

$w_{2}$ = 2×6

$w_{2}$ = 12 rpm