Physics - Description of Motion in Two and Three Dimension
Exam Duration: 45 Mins Total Questions : 30
If \(\vec {A}, \vec B \ and \ \vec C\) represent vectors denoting the sides of a cube,the size of the cube is best given by
- (a)
\((\vec A \cdot \vec B ) \cdot \vec C\)
- (b)
\((\vec A \times \vec B ) \cdot \vec C\)
- (c)
\((\vec A \cdot \vec B ) \times \vec C\)
- (d)
\((\vec A \times \vec B ) \times \vec C\)
A person at the top of a tower projects a ball vertically upward with a velocity of 29.4ms-1,4 seconds afterwards he drops a second ball and both reach the ground simultaneously.The height H and the time T for which the second ball was in air, are respectively.
- (a)
78.4 m; 4 s
- (b)
39.2 m;2s
- (c)
117.6 m;6 s
- (d)
None of the above
A projectile thrown with the speed \(\vartheta\) at an angle \(\theta\) has a range R on the surface of earth.For same \(\vartheta\) and \(\theta\) ,its range on the surface of moon will be
- (a)
\(\frac {R}{6} \)
- (b)
R
- (c)
6R
- (d)
36R
A particle reaches its highest point when it has covered exactly one-half of its horizontal range.The corresponding point on the displacement time graph is characterised by
- (a)
negative slope and zero curvature
- (b)
zero slope and negative curvature
- (c)
zero slope and positive curvature
- (d)
positive slope and zero curvature
A body is projected at an angle of 30° with the horizontal and with a speed of 30 ms-1. What is the angle with the horizontal after 1.5 seconds? (Take g = 10ms-2)
- (a)
0°
- (b)
30°
- (c)
60°
- (d)
90°
A boy can throw a stone upto a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone upto will be :
- (a)
20\(\sqrt2\)m
- (b)
10m
- (c)
10\(\sqrt2\)m
- (d)
20m
The ceiling of a hall is 40 m high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed of 56 ms-1 without hitting, the ceiling of the hall is
- (a)
25°
- (b)
30°
- (c)
45°
- (d)
60°
Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is π/3 and its maximum height is hi then the maximum height of the other will be
- (a)
3h1
- (b)
2h1
- (c)
h1/2
- (d)
h1/3
A rifle shoots a bullet with a muzzle velocity of 400 m/sec at a small target 400 metre away. The height above the target at which the bullet must be aimed to hit the target is:
- (a)
1 metre
- (b)
5 metre
- (c)
10 metre
- (d)
0.5 metre
A plane is flying horizontally at 98 m/s and releases an object which reaches the ground in 10 sec. The angle made by it while hitting the ground is:
- (a)
55°
- (b)
45°
- (c)
60°
- (d)
75°
The driver of a car travelling at 72 km h-1 , suddenly sees a big rock on the road at a distance of20 m. What can he do to avoid a collision?
- (a)
Apply brakes
- (b)
Turn sharply
- (c)
Follow a zig-zag path
- (d)
Shut the engine
A body of mass m is moving in a circle of radius r with a constant speed v. The work done by the centripetal force in moving the body over half the circumference of the circle is:
- (a)
mv2r
- (b)
zero
- (c)
mv2/r
- (d)
r2/mv2
The overbridge of a canal is in the form of a circular arc of radius R. What is the greatest speed at which a motorcyclist can cross the bridge without leaving the ground?
- (a)
\(\sqrt{5gR}\)
- (b)
\(\sqrt{3gR}\)
- (c)
\(\sqrt{2gR}\)
- (d)
\(\sqrt{gR}\)
A person with a mass of M kg stands in contact against the wall of a cylindrical drum of radius r rotating with an angular velocity co.If the coefficient of friction between the wall and the clothing is u, the minimum rotational speed of the cylinder which enables the person to remain stuck to the wall when the floor is suddenly removed is:
- (a)
\(ω_{min}=\sqrt{g\over \mu r}\)
- (b)
\(ω_{min}=\sqrt{ \mu r\over g}\)
- (c)
\(ω_{min}=\sqrt{2g\over \mu r}\)
- (d)
\(ω_{min}=\sqrt{rg\over \mu }\)
A body is just being revolved in a vertical circle of radius R with a uniform speed. The string breaks when the body is at the highest point. The horizontal distance covered by the body after the string breaks is:
- (a)
2R
- (b)
R
- (c)
R√2
- (d)
4R
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plant. It fol1ows that
- (a)
its velocity is constant
- (b)
its acceleration is constant
- (c)
its kinetic energy is constant
- (d)
it moves in a straight line
In uniform circular motion
- (a)
both velocity and acceleration are constant
- (b)
acceleration and speed are constant but velocity changes
- (c)
both acceleration and velocity change
- (d)
both acceleration and speed are constant
The earth (mass = 6 x 1024kg) revolves around the sun with an angular velocity of 2 x 10-7 radian/see in a circular orbit of radius 1.5 x 108 km. The force exerted by the sun, on the earth is:
- (a)
6x1019 N
- (b)
18x1025 N
- (c)
36x1021N
- (d)
27x1039N
A projectile is moving at 60 m/sec at its highest point where it breaks into two equal parts due to an internal explosion. One part moves up vertically at 50 m/sec with respect to the ground. The other part will move at:
- (a)
110 m/sec
- (b)
120 m/sec
- (c)
130 m/sec
- (d)
10\(\sqrt{61}\) m/sec
Two projectiles A and B thrown with speeds in the ratio 1 :√2 acquired the same heights. If A is thrown at an angle of 45° with the horizontal, the angle of projection of B will be:
- (a)
00
- (b)
600
- (c)
300
- (d)
450
A body moves in a circular path of radius r = 500 m with tangential acceleration at = 2 ms2. When its tangential linear velocity is 30 m/s, the total acceleration will be:
- (a)
5.4ms-2
- (b)
3.9 ms-2
- (c)
2.7ms-2
- (d)
2.1 ms-2
A ball is thrown up at an angle with the horizontal. Then, the total change of momentum by the instant it returns to the ground is
- (a)
acceleration due to gravity x total time of flight
- (b)
weight of the ball x half the time of flight
- (c)
weight of the ball x total time of flight
- (d)
weight of the ball x horizontal range
A particle is projected with velocity \(\sqrt{2gh}\) such that it just crosses two walls of height h and separated by h. Find the angle of projection.
- (a)
15°
- (b)
75°
- (c)
60°
- (d)
30°
If the road is unbanked and the coefficient of friction between the road and the tyres is 0.8, then the maximum speed with which an automobile can move around a curve of 84.5 m radius without slipping is:
- (a)
26 ms-1
- (b)
67.6 ms-1
- (c)
13 ms-1
- (d)
36.7 ms-1
Which motion does not require force to maintain it?
- (a)
Uniform circular motion
- (b)
Elliptical motion
- (c)
Uniform straight line motion
- (d)
Projectile motion
A fighter aircraft is looping in a vertical plane. The minimum velocity at the highest point is :
- (a)
\(\sqrt{1\over 2}gr\)
- (b)
\(\sqrt{2gr}\)
- (c)
\(\sqrt{gr}\)
- (d)
\(\sqrt{3gr}\)
The range of a projectile fired at an angle of 15° is 50 m. If it is fired with the same speed at an angle of 45°, its range will be:
- (a)
50 m
- (b)
100m
- (c)
25m
- (d)
37m