Q: A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block will be
(a) P
(b) Pm/(M+m)
(c) PM/(M+m)
(d) Pm/(M-m)
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Ans: (c)
Sol:Let force exerted by rope on the block is T , then
For block ,
T = M a …(i)
For rope ,
P – T = m a …(ii)
Adding (i) & (ii)
P = (M + m)a
$ \displaystyle a = \frac{P}{M+m}$
From (i)
$\displaystyle T = \frac{P M}{M+ m} $