A shell of mass 200 g is ejected from a gun of mass 4 g by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is

  • 100 ms-1

  • 80 ms-1

  • 40 ms-1

  • 40 ms-1


A.

100 ms-1

In the given problem conservation of linear momentum and energy hold good.
Conservation of momentum yields.

m1v1 + m2v2 = 0
4v1 + 0.2 v2  = 0

Conservation of energy yields


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Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

  • 0.5 N

  • 1.5 N

  • fraction numerator square root of 3 over denominator 4 end fraction space straight N
  • fraction numerator square root of 3 over denominator 4 end fraction space straight N


B.

1.5 N

Minimum additional force needed

F = - (Fresultant)x


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Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be

  • Mv newton

  • 2 Mv newton

  • Mv/2 Newton

  • Mv/2 Newton


A.

Mv newton

Force required,




as velocity v is constant, hence

F= Mv newton

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A block B is pushed momentarily along a horizontal surface with an initial velocity v. if μ is the coefficient of sliding friction between B  and the surface, block B will come to rest after a time:

  • v/gμ

  • gμ/v

  • g/v

  • g/v


A.

v/gμ

Block B will come to rest, if force applied to it will vanish due to frictional force acting between block B and surface, ie,

force applied = frictional force
i.e., μmg = ma
μmg = m (v/t)
t =v/μg

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A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RQ are F1, F2 and F3 respectively and are in the plane of the paper and along the directions shown, the force on the segment of QP is

  • F3 - F1-F2

  • square root of left parenthesis straight F subscript 3 minus straight F subscript 2 right parenthesis squared space plus straight F subscript 2 squared end root
  • square root of left parenthesis straight F subscript 3 minus straight F subscript 1 right parenthesis squared minus straight F subscript 2 squared end root
  • square root of left parenthesis straight F subscript 3 minus straight F subscript 1 right parenthesis squared minus straight F subscript 2 squared end root

B.

square root of left parenthesis straight F subscript 3 minus straight F subscript 2 right parenthesis squared space plus straight F subscript 2 squared end root
F4 sin θ = F2
F4 cos θ = (F3-F1)

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