A projectile can have the same range R for two angles of projection. If t₁ and t₂ be the times of flights in the two cases, then the product of the two time of flights is proportional to

• R²

• 1/R²

• 1/R

• 1/R

An annular ring with inner and outer radii R₁ and R₂ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F_1/F₂ is

• R₁/R₂

• (R₁/R₂)²

• 1

• 1

3.

A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

• 
• 
• 
• 

The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

• 2sinφ

• 2cosφ

• 2tanφ
• 2tanφ

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

• 3.0 cm

• 2.0 cm

• 1.5 cm

• 1.5 cm

Out of the following pair, which one does NOT have identical dimensions is

• angular momentum and Planck’s constant

• impulse and momentum

• moment of inertia and moment of a force

• moment of inertia and moment of a force

The relation between time t and distance x is t=ax² +bx where a and b are constants. The acceleration is

• −2abv²

• 2bv³

• −2av³

• 2av²

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S, then

• S=ft

• S= ft²/72

• S = 1/2 ft²

• S = 1/2 ft²

A particle is moving eastwards with a velocity of 5 m/s in 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is

• towards north-east
• towards north.

• zero

• zero

A parachutist after bailing outfalls 50 m without friction. When a parachute opens, it decelerates at 2 m/s². He reaches the ground with a speed of 3 m/s. At what height, did he bail out?

• 91 m

• 182 m

• 293 m

• 293 m