### Mathematics - Dynamics

#### 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