A force F = bt (where b is a constant) is applied at an angle to a mass m kept on a smooth horizontal plane. The velocity of mass m at the moment of its breaking off the plane is
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a
mg2cosα2bsin2α
b
g2cosα2mbsin2α
c
mg2sin2α2bcosα
d
bg2cosα2msinα
answer is A.
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Detailed Solution
btcosα=mdvdt ......(i)N+btsinα=mg ........(ii)For breaking off N=0 Therefore from (ii), t=mgbsinα=t0 (say) From (i), m∫0v dv=(bcosα)∫0t0 tdtmv=(bcosα)t022=(bcosα)2m2g2b2sin2αv=mg2cosα2bsin2α