Question

A mass of 2 kg is whirled in a horizontal circle by means of string at an initial speed of 5 r.p.m . Keeping the radius constant the tension of string is doubled. The new speed is nearly

Answer 1

Given :
mass=2kg

Initial speed=ω=5rpm=5x2π/60 rad/sec =π/6 rad/sec

Tension=Centripetal force= mrω²

T=2xrx(π/6)²

T =mrω²=2xrxπ²/36--------- equation 1

If tension is doubled, centripetal force also will be doubled .

2T=mrω₁²=2x[2xrxπ²/36] ----- equation 2

where ω₁² is the new angular speed 

Dividing equation 2 by 1 we get 

ω₁²=2ω²
ω₁=√2ω=√2x5≈7rpm

∴New angular speed will be √2 times initial angular speed

Answer 2

It's the Q.11 pls don't get confused

Hope it helps