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

• R

D.

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

• R₂/R₁

A.

R₁/R₂

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

• 
• 
• 
• 

A.

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

• tanφ

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

• 1.0 cm

D.

1.0 cm