If force (F), velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are
[FvT^{-1}]
[FvT^{-2}]
[Fv^{-1}T^{-1}]
[Fv^{-1}T^{-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 m_{1}, m_{2} and m_{3} connected by a string passing over a pulley P. The mass m_{1} hangs freely and m_{2} and m_{3} are on a rough horizontal table (the coefficient of friction = μ). the pulley is frictionless and of negligible mass. The downward acceleration of mass m_{1} 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,
mv^{2}
2mv^{2}
2mv^{2}
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/s^{2} 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 10^{24} kg) have to be compressed to be a black hole?
10^{-9} m
10^{-6} m
10^{-2} m
10^{-2} m