Mathematics - Dynamics
Exam Duration: 45 Mins Total Questions : 20
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
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
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
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
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
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)
\(8\sqrt { h{ h }^{ \prime } } \)
A particle is projected with a given horizontal range;then number of directions in which the particle can be projected, is
- (a)
4
- (b)
3
- (c)
2
- (d)
1
A ball is projected with a velocity of 9.8 m/sec at a plane where g = 9.8 m/\({ sec }^{ 2 }\). The maximum range of the projectile on the horizontal ground, is
- (a)
100 m
- (b)
10 m
- (c)
98 m
- (d)
9.8 m
If you want to kick a football to the maximum distance, then the angle at which it should be kicked is
- (a)
45°
- (b)
90°
- (c)
30°
- (d)
60°
A particle is projected vertically upwards and is at a height h after \({ t }_{ 1 }\)seconds and again after \({ t }_{ 2 }\)seconds. Then h equals
- (a)
\(\frac { { t }_{ 1 }{ t }_{ 2 } }{ 2g } \)
- (b)
\(\frac { { t }_{ 1 }{ t }_{ 2 } }{ g } \)
- (c)
\(\frac { 1 }{ 2 } g{ t }_{ 1 }{ t }_{ 2 }\)
- (d)
\(g{ t }_{ 1 }{ t }_{ 2 }\)
Two stones are projected from the top of a cliff h metres high, with the same speed u so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle \(\theta \) to the horizontal, then \(\theta \) equals
- (a)
\(2g\sqrt { u/h } \)
- (b)
\(2h\sqrt { u/g } \)
- (c)
\(u\sqrt { 2/gh } \)
- (d)
\(\sqrt { 2u/gh } \)
Let \({ R }_{ 1 }\)and \({ R }_{ 2 }\) respectively be the maximum ranges up and down an inclined plane and \({ R }_{ 3 }\)be the maximum range on the horizontal plane. Then \({ R }_{ 1 },\quad { R }_{ 3 },\quad { R }_{ 2 }\) are in
- (a)
A.P.
- (b)
G.P.
- (c)
H.P.
- (d)
Arithmetic geometric progression
A particle is projected up a smooth inclined plane, the angle of inclination of the plane is \(\theta \), along the line of the greatest slope. The particle comes to rest after t second, then the velocity of projection, is
- (a)
\((gsin\theta )t\)
- (b)
\(\frac { 1 }{ 2 } (gsin\theta )t\)
- (c)
\(\frac { 1 }{ 2 } (gcos\theta )t\)
- (d)
\(\frac { 1 }{ 2 } ({ g }^{ 2 }sin\theta )t\)
A particle is projected up a smooth inclined plane whose angle of inclination with the horizontal plane is 30°. The particle comes to rest after 2 seconds; then the velocity of projection, is (where g = 9.8/\({ sec }^{ 2 }\))
- (a)
4.9 m/sec
- (b)
9.8 m/sec
- (c)
19.6 m/sec
- (d)
NONE OF THESE
The time of flight of a projectile with horizontal range R is T, then angle of projection of the projectile, is given by
- (a)
\({ tan }^{ -1 }\left( \frac { 2g{ T }^{ 2 } }{ R } \right) \)
- (b)
\({ tan }^{ -1 }\left( \frac { g{ T }^{ 2 } }{ R } \right) \)
- (c)
\({ tan }^{ -1 }\left( \frac { gT }{ R } \right) \)
- (d)
\({ tan }^{ -1 }\left( \frac { g{ t }^{ 2 } }{ 2R } \right) \)
Particles are projected from a point O, in the vertical plane with velocity \(\sqrt { 2gh } \), then the locus of the vertices of their paths is
- (a)
an ellipse
- (b)
a parablola
- (c)
a circle
- (d)
NONE OF THESE
A paraticle is projected upward with velocity 10 m/s along a plane inclined to the horizontal at an angle of 30°, the angle of projection being 60°. Then range of the projectile along the plane is
- (a)
5.8 m
- (b)
6.8 m
- (c)
7.8 m
- (d)
7 m
A particle is projected with initial velocity u. If the greatest hight attained by the particle be H, then the range R on the horizontal plane through the point of projection is
- (a)
\(4\sqrt { 1+\left( \frac { { u }^{ 2 } }{ 2g } +H \right) } \)
- (b)
\(2\sqrt { H\left( \frac { { u }^{ 2 } }{ 2g } +H \right) } \)
- (c)
\(2\sqrt { H\left( \frac { { u }^{ 2 } }{ 2g } -H \right) } \)
- (d)
\(4\sqrt { H\left( \frac { { u }^{ 2 } }{ 2g } -H \right) } \)
A particle is projected down an inclined plane, the inclination of the plane being \(\beta \), with an initial velocity u and angle of projection is \(\alpha (\alpha >\beta );\) then the time of flight of the projectile, is
- (a)
\(\frac { 2usin(\alpha +\beta ) }{ gcos\beta } \)
- (b)
\(\frac { 2usin(\alpha -\beta ) }{ gcos\beta } \)
- (c)
\(\frac { 2usin\alpha }{ gcos\beta } \)
- (d)
\(\frac { 2usin\left( \alpha -\beta \right) }{ gsin\beta } \)