# 1) Three equal masses P, Q and R are pulled with a constant force F. They are connected to each other with strings. The ratio of the tension between PQ and QR is:(answer should come 2:1)2) The pulleys and strings shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle Ф should be (answer should come 45 degree)3) A string of negligible mass going over a clamped pulley of mass 'm' supports a block of mass M as shown in figure. The force on the pulley by the clamp is given by {answer should come 4) When a bus suddenly takes a turn, the passengers are thrown outwards because of----------5) A body of mass m stands on one end of a wooden plank of length L and mass M. The plank is floating on water. If the boy walks from one end of the plank to the other end at a constant peed, the resulting displacement of the plank is given by (answer should come )

1
by alwaz

2014-12-15T18:43:53+05:30

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1) Tension in string between P and Q = T1
tension in string between Q and R = T2
let all of them move with a uniform acceleration of  a.
let mass of P , Q and R be  m.
F - T1 = m a     for  P
T1 - T2 = m a    for Q
T2 = m a   for R
=> T1 = ma + ma = 2 ma
F = 3 ma
ratio = 2

2)
T1 = m g
T1 Sin Ф + T2 Cos Ф = √2 m g
T2 = m g
Sin Ф + Cos Ф = √2
square it,      1 + sin 2Ф = 2
Sin 2Ф = 1     => Ф = 45 deg

3)

there are vertical forces M g (same as tension T) and m g  weight of pulley.  there is a horizontal force   Mg = Tension.
resultant force =  √ [ (Mg+mg)² + (Mg)² ]

4)   inertia of motion.    There is not enough centripetal force acting on them. So they continue to move in a straight line.

5)
Center of mass of  body m and plank of mass M is at   [ M * L/2 + m * 0 ] / (M+m) , from the end where the body m is present.
that is = CM at   ML/2(M+m)
We assume there is no friction between water and plank.
When the body goes to the other end, the center of mass will be at ML/2(M+m) from that end.
Since there is no external force on the two body  system together, the CM stays at the same point.
Hence the plank moves by L - ML/2(M+m)  - ML/2(M+m) = L * m /(M+m)

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