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Q.

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

mg2cos⁡α2bsin2⁡α

b

g2cos⁡α2mbsin2⁡α

c

mg2sin2⁡α2bcos⁡α

d

bg2cos⁡α2msin⁡α

answer is A.

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Detailed Solution

btcos⁡α=mdvdt    ......(i)N+btsin⁡α=mg    ........(ii)For breaking off N=0 Therefore from (ii), t=mgbsin⁡α=t0 (say)  From (i), m∫0v dv=(bcos⁡α)∫0t0 tdtmv=(bcos⁡α)t022=(bcos⁡α)2m2g2b2sin2⁡αv=mg2cos⁡α2bsin2⁡α
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