If force (F), velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are

• [FvT^-1]

• [FvT^-2]

• [Fv^-1T^-1]

• [Fv^-1T^-1]

A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle  with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is,

• 3.5

• 5.9

• 16.3

• 16.3

A particle is moving such that its position coordinates (x,y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2 sec and (13 m, 14m) at time t= 5 sec. Average velocity vector (v_av) from t = 0 to t = 5 s is,

A system consists of three masses m₁, m₂ and m₃ connected by a string passing over a pulley P. The mass m₁ hangs freely and m₂ and m₃ are on a rough horizontal table (the coefficient of friction = μ). the pulley is frictionless and of negligible mass. The downward acceleration of mass m₁ is,

The force F acting on a particle of mass m is indicated by the force-time graph as shown below. The climate change in momentum of the particle over the time interval from zero to 8 s is,

• 24 Ns

• 20 Ns

• 12 Ns

• 12 Ns

A balloon with mass m is descending down with an acceleration a (where a <g). How much mass should be removed from it so that it starts moving up with an acceleration a?

A body of mass (4m) is lying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed (v). The total kinetic energy generated due to explosion is,

• mv²

• 

• 2mv²

• 2mv²

8.

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 rev/s² is,

• 25 N

• 50 N

• 78.5 N

• 78.5 N

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle  without slipping and slipping down the incline without rolling is,

• 5:7

• 2:3

• 2:5

• 2:5

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 x 10²⁴ kg) have to be compressed to be a black hole?

• 10^-9 m

• 10^-6 m

• 10^-2 m

• 10^-2 m