Multiple Choice QuestionsA particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λA to λB after the collision is
D.
A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
2g/3
g/2
5g/6
5g/6
B.
g/2
For the mass m,
mg-T = ma
As we know, a = Rα ... (i)
So, mg-T = mRα
Torque about centre of pully
T x R = mR2α ...... (ii)
From Eqs. (i) and (ii), we get
a = g/2
Hence, the acceleration of the mass of a body fall is g/2.
A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to
44%
50%
56%
56%
C.
56%
It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of pd and pc are respectively :
(0,1)
(.89,.28)
(.28,.89)
(0,0)
B.
(.89,.28)
For collision of a neutron with deuterium:
Applying conservation of momentum:
mv + 0 = mv1 + 2mv2 .....(i)
v2 -v1 = v ...... (ii)
Therefore, Collision is elastic, e = 1
From equ (i) and equ (ii) v1 = -v/3
Now, for the collision of neutron with carbon nucleus
Applying conservation of momentum
mv + 0 = mv1 + 12mv2 ....; (iii)
v = v2-v1 ....(iv)
Given in the figure are two blocks A and B of weight 20 N and 100 N respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is
100N
80 N
120 N
120 N
C.
120 N
In the vertical direction, weight are balanced by frictional forces.
As the blocks are in equilibrium balance forces are in horizontal and vertical direction.
For the system of blocks (A+B)
F = N
For block A, fA = 20 N and for block B.
fB = fA +100 = 120 N
