Mathematics - Dynamics

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Question - 1

The force required to accelerate a train of mass \({ 10 }^{ 6 }\)kg from rest to a velocity of 6m/second in 2 minutes, is

  • A \(4\times { 10 }^{ 4 }N\)
  • B \(5\times { 10 }^{ 4 }N\)
  • C \(6\times { 10 }^{ 4 }N\)
  • D None of these

Question - 2

A bullet of mass 20 grams fired into a wall with a velocity of 10m/sec loses all its velocity in one second. Then distance covered by the bullet in the wall is

  • A 3 m
  • B 4 m
  • C 5 m
  • D 6 m

Question - 3

A man of weight 60 kg jumps off a railway train running on horizontal rails at 20 km/hr with a packet of 10 kg in his hand. The thurst of the packet on his hand, is

  • A 0
  • B 50 kg wt
  • C 10 kg wt
  • D 70 kg wt

Question - 4

A particle is projected under gravity (g=9.81 m/\({ sec }^{ 2 }\)) with a velocity of 29.43 m/sec at an elevation of 30°. The times of flight in seconds, to a height of 9.81 m in second, are

  • A 0.5, 1.5
  • B 1,2
  • C 1.5, 2
  • D 2,3

Question - 5

The angle of projection of a particle when its range on the horizontal plane is \(4\sqrt { 3 } \) times the greatest height attained is

  • A 15°
  • B 30°
  • C 45°
  • D 60°

Question - 6

From the top of a tower of height 100 m, a ball is projected with a velocity of 10 m/sec. It takes 5 seconds to reach the ground. If g=10 m/\({ sec }^{ 2 }\), then the angle of projection is

  • A 30°
  • B 45°
  • C 60°
  • D 180°

Question - 7

A particle is projected with a velocity of 39.2 m/sec at an angle of 30° to the horizontal. It will move at right angles to the direction of projection, after the time

  • A 8 sec
  • B 5 sec
  • C 6 sec
  • D 10 sec

Question - 8

A cannon ball has a range R on a horizontal plane. If h and \({ h }^{ \prime }\)are the greatest heights in the two possible paths, then R equals

  • A \(\sqrt { 4h{ h }^{ \prime } } \)
  • B \(\sqrt { 8h{ h }^{ \prime } } \)
  • C \(4\sqrt { h{ h }^{ \prime } } \)
  • D \(8\sqrt { h{ h }^{ \prime } } \)

Question - 9

If R is the horizontal range of a projectile and h the greatest height, then velocity of projection is

  • A \(g\left( h+\frac { { R }^{ 2 } }{ 16h } \right) \)
  • B \(2g\left( h+\frac { { R }^{ 2 } }{ 16h } \right) ^{ 1/2 }\)
  • C \(2g\left( h+\frac { R }{ 16h } \right) \)
  • D NONE OF THESE

Question - 10

If 4 seconds be the time in which a projectile reaches a point in the path and 5 seconds be the time from P till it reaches the horizontal plane through the point of projection, then the height of the point P above the horizontal plane in metres, is

  • A 40
  • B 98
  • C 196
  • D NONE OF THESE
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