A block of mass m is projected on a smooth horizontal circular track with speed v. What is the average normal force (in Newtons) exerted by circular walls on the block during its motion from A to B?
A
2√2mv2πR
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B
mv22πR
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C
mv2√2πR
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D
mv2R
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Solution
The correct option is A2√2mv2πR ∵ Avg. normal force = Rate of change in momentum during its motion from A to B
FN=Δ(mv)Δt Velocity at point A is v^i Velocity at point B is v^j Time taken to move A to B Δt=(2πR)4v=πR2v FN=mΔvΔt=m(v^j−v^i)(πR)(2v) |FN|=2mvπR×√v2+v2=2√2mv2πR |FN|=2√2mv2πRN