A block is kept on a frictionless inclined surface with angle of inclination α. The incline is given an acceleration a to keep the block stationary. Then a is equal to

• g/tanα

• g cosecα

• g

• g

A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function time is given by

3.

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

• x²

• e^x

• x

• x

A ball is thrown from a point with a speed ν₀ at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed ν₀/2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

• yes, 60°

• yes, 30°

• no

• no

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

A person observes that the full length of a train subtends an angle of 15°. If the distance between the train and the person is 3 km, the length of the train, calculated using parallax method, in meters is

• 45

• $45 \mathrm{\pi }$

• $250 \mathrm{\pi }$

• $75 \mathrm{\pi }$

The following figure gives the movement of an object. Select the correct statement from the given choices.

• The total distance travelled by the object is 975 m

• The maximum acceleration of the object is 2m/s²

• The maximum deceleration happend between 25th and 85th seconds

• The object was at rest between 10th and 15th seconds

Two object P and Q, travelling in the same direction starts from rest. While the object P starts at time t = 0 and object Q starts later at t = 30 min. The object P has an acceleration of 40 km/h². To catch P at a distance of 20 km, the acceleration of Q should be

• 40 km/h²

• 80 km/h²

• 160 km/h²

• 120 km/h²

A train of length L move with a constant speed V_t. A person at the back of the train fires a bullet at time t = 0 towards a target which is at a distance of D (at time t = 0) from the front of the train (on the same direction of motion). Another person at the front of the train fires another bullet at time t = T towards the same target. Both bullets reach the target at the same time. Assuming the speed of the bullets V_b are same, the length of the train is

• T × (V_b × 2V_t)

• T × (V_b + V_t)

• $\frac{2{\mathrm{V}}_{\mathrm{b}}\mathrm{D}}{{\mathrm{V}}_{\mathrm{b}} + {\mathrm{V}}_{\mathrm{t}}} + \mathrm{T} \left({\mathrm{V}}_{\mathrm{b}} - {\mathrm{V}}_{\mathrm{t}}\right)$

• T × (V_b − 2V_t)

A person from a truck, moving with a constant speed of 60 km/h, throws a ball upwards with a speed of 60 km/h. Neglecting the effect of Earth and choose the correct answer from the given choice.

• The person cannot catch the ball when it comes down since the truck is moving

• The person can catch the ball when it comes down, if the truck is stopped immediately after throwing the ball

• The person can catch the ball when it comes down, if the truck continues to move with a constant speed of 60 km/h

• The person can catch the ball when it comes down, if the truck moves with speed more than 60 km/h