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 Multiple Choice QuestionsMultiple Choice Questions

31.

A 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

  • straight lambda subscript straight A over straight lambda subscript straight B space equals space 2 over 3
  • straight lambda subscript straight A over straight lambda subscript straight B space equals space 1 half
  • straight lambda subscript straight A over straight lambda subscript straight B space equals space 1 third
  • straight lambda subscript straight A over straight lambda subscript straight B space equals space 1 third

D.

straight lambda subscript straight A over straight lambda subscript straight B space equals space 1 third


By conservation of linear momentum
mv space equals space mv subscript 1 space plus straight m over 2 straight v subscript 2
2 straight v space equals space 2 straight v subscript 1 space plus straight v subscript 2 space... space left parenthesis 1 right parenthesis
By space law space of space collision
straight e space equals fraction numerator straight v subscript 2 minus straight v subscript 1 over denominator straight u subscript 1 minus straight u subscript 2 end fraction
straight u space equals space straight v subscript 2 minus straight v subscript 1 space space... space left parenthesis 2 right parenthesis
by space equ. space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis
straight v subscript 1 space equals space straight v over 3 semicolon space straight v subscript 2 space equals space fraction numerator 4 straight v over denominator 3 end fraction
straight lambda subscript 1 space equals space straight h over straight p subscript 1 semicolon space straight lambda subscript 2 space equals space straight h over straight o subscript 2
straight lambda subscript 1 over straight lambda subscript 2 space equals space 2 over 1
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32.

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.

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33.

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%

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34.

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

Pd = 12mv2 -12mv1212mv2 = 89 = 0.89

Now, for the collision of neutron with carbon nucleus

Applying conservation of momentum

mv + 0 = mv1 + 12mv2 ....; (iii)

v = v2-v1  ....(iv)

v1 = -1113 vPc = 12mv2 - 12m1113v212mv2 = 48169 0.28


35.

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

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