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