Home
Class 12
PHYSICS
A small ball is rolled with speed u from...

A small ball is rolled with speed `u` from piont A along a smooth circular track as shown in figure. If `x=3R`, then

Determine the required speed u so that the ball returns to A, the point of projection after passing through C, the highest point.

Text Solution

Verified by Experts

We determine the velocity at `C` so that it reaches `A` along a parbolic trajectory, then applying the law of conservation of energy to the motion `ABC` (as non-conservative force are absent)
`v=` velocity at point `C=(3)/(2)sqrt(gR)`
applying conservation of energy from `A` to `C`
`(1)/(2)mu^(2)=2mgR+(1)/(2)mv^(2)`
`rArr u=(5)/(2)sqrt(gR)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A small ball is rolled with speed u from piont A along a smooth circular track as shown in figure. If x=3R , then What is the minimum value of x for which the ball can reach the point of projection after reaching C?

A small spherical ball is released from a point at a height h on a rough track shown in figure. Assuming that it does not slip anywhere, find its linear speed when it rolls on the horizontal part of the track.

A ball of mass m is released from A inside a smooth wedge of mass m as shown in figure. What is the speed of the wedge when the ball reaches point B?

A smooth circular table is surrounded by a rim whose interior is vertical . A ball is projected along the table from a point on the rim in a direction making an angle theta to the radius through the point and returns to the point of projection after two impacts . If e be the coefficient of restitution, then

A particle of mass m is projected with speed sqrt(Rg/4) from top of a smooth hemisphere as shown in figure. If the particle starts slipping from the highest point, then the horizontal distance between the point where it leaves contact with sphere and the point at which the body was placed is

A small ball is pushed from a height h along a smooth hemispherical bowl of radius R. With what speed should the ball be pushed so that it just reaches the top of the opposite end of the bowl?

A cylindrical hall has a horizontal smooth floor. A ball is projected along the floor from A point on the wall in a direction making an angle theta with the radius through the point the ball returns bak to the initial point after two impacts with the wall. if the coefficient of restitution is e than tan^(2)theta will be

A small ball is projected from point P towards a vertical wall as shown in Fig. It hits the wall when its velocity is horizontal. Ball reaches point P after one bounce on the floor. The coefficient of restitution assuming it to be same for two collisions is n//2 . All surfaces are smooth. Find the value of n .

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

A small block is projected with a speed v_( 0) on a horizontal track placed on a sufficiently rough surface which turns into a semi circle ( vertical) of radius R. Find the min value of V_(o) so that the body will hit the point A after leaving the track at its highest point. The arrangement is shown in the figure, given that the straight part is rough & the curved path is smooth. The coefficient of friction is mu .