Q. No.A ship AA is moving westward with a speed of 10 kmph10 kmph and a ship B,B, 100 km100 km south of A,A, is moving northward with a speed of 10 kmph.10 kmph. The time after which the distance between them becomes the shortest is:
1. 0 h0 h
2. 5 h5 h
3. 5√2 h5√2 h
4. 10√2 h10√2 h
Two particles AA and BB, move with constant velocities →v1→v1 and →v2→v2 respectively. At the initial moment, their position vectors are →r1→r1 and →r2→r2 respectively. The conditions for particles AA and BB for their collision will be:
| 1. | →r1−→r2|→r1−→r2|=→v2−→v1|→v2−→v1|→r1−→r2|→r1−→r2|=→v2−→v1|→v2−→v1| |
| 2. | →r1⋅→v1=→r2⋅→v2→r1⋅→v1=→r2⋅→v2 |
| 3. | →r1×→v1=→r2×→v2→r1×→v1=→r2×→v2 |
| 4. | →r1−→r2=→v1−→v2→r1−→r2=→v1−→v2 |
→R=4sin(2πt)ˆi+4cos(2πt)ˆj,→R=4sin(2πt)^i+4cos(2πt)^j,
where RR is in metres, tt is in seconds and ˆi,ˆj^i,^j denotes unit vectors along xx and y-y-directions, respectively. Which one of the following statements is wrong for the motion of the particle?
| 1. | Acceleration is along (-→R). |
| 2. | Magnitude of the acceleration vector is v2R, where v is the velocity of the particle. |
| 3. | Magnitude of the velocity of the particle is 8 m/s. |
| 4. | Path of the particle is a circle of radius 4 m. |
A projectile is fired from the surface of the earth with a velocity of 5 m/s and at an angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory that is identical to the trajectory of the projectile fired from the Earth. The value of the acceleration due to gravity on the other planet is: (given g=9.8 m/s2 )
1. 3.5 m/s2
2. 5.9 m/s2
3. 16.3 m/s2
4. 110.8 m/s2
The velocity of a projectile at the initial point A is 2ˆi+3ˆj m/s. Its velocity (in m/s) at the point B is:
| 1. | −2ˆi+3ˆj | 2. | 2ˆi−3ˆj |
| 3. | 2ˆi+3ˆj | 4. | −2ˆi−3ˆj |
1. θ=tan−1(14)
2. θ=tan−1(4)
3. θ=tan−1(2)
4. θ=45∘
A particle moves in a circle of radius 5 cm with constant speed and time period 0.2π s. The acceleration of the particle is:
| 1. | 25 m/s2 | 2. | 36 m/s2 |
| 3. | 5 m/s2 | 4. | 15 m/s2 |
A body is moving with a velocity of 30 m/s towards the east. After 10 s, its velocity becomes 40 m/s towards the north. The average acceleration of the body is:
1. 7 m/s2
2. √7 m/s2
3. 5 m/s2
4. 1 m/s2
A missile is fired for a maximum range with an initial velocity of 20 m/s. If g=10 m/s2, then the range of the missile will be:
| 1. | 50 m | 2. | 60 m |
| 3. | 20 m | 4. | 40 m |
A projectile is fired at an angle of 45∘ with the horizontal. The elevation angle α of the projectile at its highest point, as seen from the point of projection is:
1. 60∘
2. tan−1(12)
3. tan−1(√32)
4. 45∘
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