Masses `M_1`, `M_2` and `M_3` are connected by strings of negligible mass which pass over massless and friction less pulleys `P_1` and `P_2` as shown in fig The masses move such that the portion of the string between `P_1` and `P_2` in parallel to the inclined plane and the portion of the string between `P_2` and `M_3` is horizontal. The masses `M_2` and `M_3` are 4.0kg each and the coefficient of kinetic friction between the masses and the surfaces is 0.25. The inclined plane makes an angle of `37^@` with the horizontal.

If the mass `M_1` moves downwards with a uniform velocity, find
(i) the mass of `M_1`
(ii) The tension in the horizontal portion of the string `(g=9.8 m//sec^2, sin 37^@=3//5)`

Answer

B, D

Explanation

(a) If `M_1`, `M_2` and `M_3` are considered as a system, then the force responsible to more them is `M_1g` and the retarding force is `(M_2gsintheta+muM_2gcostheta+muM_3g)`. These two should be equal as the system is moving with constant velocity.