Motion in a Pla...

Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first?

At the top of the trajectory of a projectile, the direction of its velocity and acceleration are

For a projection, (range)² is 48 times of (maximum height )² obtained. Find angle of projection.

A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical support. About the point of suspension,

A particle is moving uniformly in a circular path of radius r. When it moves through an angular displacement θ, then the magnitude of the corresponding linear displacement will be

A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of 15° in time t sec. The increase in angle through which it rotates in the next 2t sec is

The front wheel on an ancient bicycle has radius 0.5 m. It moves with an angular velocity given by the function ω(t) = 2 + 4t² , where t is in sec. About how far does the bicycle move between t = 2 s and t = 3 s?

A hoop of radius r and mass m rotating with an angular velocity ω₀ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

Two cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂ respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal accelerations is