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Average torque on a projectile of mass m initial speed u and angle of projection theta between initial and final positions P and Q as shown in the figure about the point of projection is Average torque on a projectile of mass m initial speed u and angle of projection theta between initial and final [...]

A homogenous rod of length l = ηx and mass M is lying on a smooth horizontal floor. A bullet of mass m hits the rod at a distance x from the middle of the rod at a velocity v0 perpendicular to the rod and comes to rest after collision. If the velocity of the [...]

Two identical uniform solid spherical balls `A` and `B` of mass `m` each are placed on a the fixed wedge as shown in figure. Ball `B` is kept at rest and it is released just before two balls collides. Ball `A` rolls down without slipping on inclined plane and collide elastically with ball `B`. The [...]

A uniform smooth rod (mass `m` and length `l`) placed on a smooth horizontal floor is it by a particle (mass `m`) moving on the floor, at a distance `l/4` from one end elastically `(e = 1)`. The distance travelled by the centre of the rod after the collision when it has completed three revolutions [...]

A particle of mass m is rigidly attached at A to a ring of mass 3m and radius r. The system is released from rest and rolls without sliding. The angular acceleration of ring just after release is A particle of mass m is rigidly attached at A to a ring of mass 3m and [...]

An impulse J is applied on a ring of mass m along a line passing through its centre O. The ring is placed on a rough horizontal surface. The linear velocity of centre of ring, once it starts rolling without slipping, is An impulse J is applied on a ring of mass m along a [...]

A uniform disk turns at 2.4 rev/s around a frictionless axis. A non rotating rod, of the same mass as the disk and length equal to the disk’s diameter is dropped onto the freely spinning disk (see the figure). They then both turn around the axis with their centres superposed. What will be the angular [...]

In both the figures all other factors are same, except that in figure (i) AB is rough and BC is smooth while in figure (ii) AB is smooth and BC is rough. In figure (i), if a sphere is released from rest it starts rolling. Now consider the figure (ii), if same sphere is A [...]

Figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the comon axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances travelled by A and B in the same time interval, then A Disc of [...]

A plank P is placed on a solid cylinder S, which rolls on a horizontal surface. The two are of equal mass. There is no slipping at any of the surfaces in contact. The ratio of kinetic energy of P to the kinetic energy of S is A plank P is placed on a solid [...]