.If the escape velocity of a rocket from the surface of the Earth is ve , then the escape velocity of the same rocket from the surface of a planet whose acceleration due to gravity as well as radius are 3 times that of the Earth is
 
 1) v_e
 2) v_e / 3
 3) 3 v_e
 4) 9 v_e

A small particle of mass m is projected at an angle θ with the X–axis with an initial velocity v_o in the X–Y plane as shown in the figure. At a time

An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by  where v is the instantaneous speed. The time taken by the object, to come to rest, would be

1) 1 s 2) 2 s  3)  4 s  4)  8s

An ant goes from P to R on a circular path in 20 second Radius OP=10m. What is the average speed and average velocity of it ?

1) (π/6) m/s, 3 m/s 2) (π/3) m/s, √3/2 3) (π/3) m/s,√3 4)  π √6

A small block of mass 0.1kg lies on the a fixed inclined plane PQ which makes an angle θ with the horizontal. A horizontal force of 1N acts on the block through its centre of mass as shown in figure. Block remains stationary if (take g= 10 m/s² )

1)  θ = 45°   
2) θ > 45° and a frictional force acts on the block towards P
3) θ < 45° and a frictional force acts on the block towards Q
4) none

A solid cylinder of radius R made of a material of thermal conductivity K₁ is surrounded cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K₂. The two ends of the combined system are maintained at two different temperatures. Then there is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

In a reversible ideal engine, 650 J of heat comes from source of 450 K, heat rejected to sink at 225 K is

1) 325 J
2) 625 J
3) 700 J
4) 800 J

A chain is held on a friction-less table with one third of its length hanging over the edge. The total length of the chain is 1 and its mass is m. Find the work required to pull the hanging part back to the table.

1) 2mgl    2) mgl / 5    3) mgl / 9   4) mgl / 18  

What is the equivalent resistance between A and B in the given circuit?

1) 4 ?
2) 2 ?
3) 8/3 ? 
4) 3/8 ?

A block of mass 1 kg slides down on a rough inclined plane of inclination 60^o starting from its top. If the coefficient of kinetic friction is 0.5 and length of the plane is 1 m, then work done against friction is  (Take g = 9.8 m/s²)

1) 9.82 J

2) 4.94 J

3) 2.45J

4) 1.96 J