Home
Class 12
PHYSICS
The cue stick hits a cue ball horizontal...

The cue stick hits a cue ball horizontally a distance `x` above the centre of the ball. Find the value of `x` for which the cue ball will instantaneously roll without slipping. Calculate the answer in terms of the radius `R` of the ball.

Text Solution

Verified by Experts

The horizontal force creates a linear impulse and angular impulse.`I=intFdt``J=inttaudt=lh`Linear impulse = change in linear momentum `rArr I=MV_(Cm)-0`..(i) Angular impulse about CM = change in angular momentum `J=lh=2/5mr^2omega-0`..(ii)Dividing (ii) and(i) we get `h=(2Mr^2omega)/(5MV_(CM))` Using `V_(CM)=romega``h=R/5R`.
Promotional Banner

Topper's Solved these Questions

  • SYSTEM OF A PARTICLES & ROTATIONAL MOTION

    VMC MODULES ENGLISH|Exercise SOLVED EXAMPLES|20 Videos

  • SYSTEM OF A PARTICLES & ROTATIONAL MOTION

    VMC MODULES ENGLISH|Exercise PRACTICE EXERCISE-1|4 Videos

  • SIMPLE HARMONIC MOTION

    VMC MODULES ENGLISH|Exercise 7-previous year question|46 Videos

  • SYSTEM OF PARTICLES AND ROTATIONAL MOTION

    VMC MODULES ENGLISH|Exercise IMPECCABLE|56 Videos

Similar Questions

Explore conceptually related problems

A solid sphere of mass M and radius R is hit by a cue at a height h above the centre C. for what value of h the sphere will rool without slipping ?

A billiard ball, initially at rest, is given a sharp impulse by a cue. The cue is held horizontally a distance h above the centre line as shown in figure. The ball leaves the cue with a speed v_(0) and because of its forward english (backward slipping) eventually acquires a final speed (9)/(7)v_(0) show that h=(4)/(5)R Where R is the radius of the ball.

A ball is projected from ground with a speed 70m//s at an angle 45^(@) with the vertical so that it strikes a vertical wall at horizontal distance (490)/(3)m from the point of projection. If the ball returns back to the poin tof projection without any collision with ground then find the coefficient of restitution between the ball and wall.

A ball is thrown with the velocity u at an angle of alpha to the horizon. Find (i) the height of which the ball will rise to (ii) the distance x from the point of projection to the point where it reaches to the ground and (iii) the time during which the ball will be in motion (neglect the air resistance ).

A uniform wheel of radius R is set lying on a rough horizontal surface is hit by as cue is such a way that the line of action passes thruogh the centre of the shell. As a result the shelll starts movign with a linear speed v without any initial angular velocity. Find the linear speed of the shell after it starts pure rolling on the surface.

Touching a hemispherical dome of radius R there is a vertical tower of height H = 4 r . A boy projects a ball horizontally at speed u from the top of the tower. The ball strikes the dome at a height (R)/(2) from ground and rebounds. After rebounding the ball retraces back its path into the hands of the boy. Then the value of u is :

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, travelling with a velocity V m//s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The velocity V of the bullet is

In order to get a billiard ball to roll without sliding from the start, where should the cue hit ? Calculate the height from centre of the sphere. Take R as the radius of sphere.

A uniform ball of radius R rolls without slipping between the rails such that the horizontal distance is sqrt(3)R between the two contact points of te rails of the ball. Figure (a) shows front view of the ball and figure (b) shows the side view of the ball. v_(CM) is the velocity of centre of mass of the ball and omega is the angular velocity of the ball after rolling down a distance 2h along the incline then

Two friends A and B (each weighing 40 kg ) are sitting on a frictionless platform some distance d apart. A rolls a ball of mass 4 kg on the platform towards B which B catches. Then B rolls the ball towards A and A catches it. The ball keeps on moving back and forth between A and B . The ball has a fixed speed of 5 m//s on the platform. a. Find the speed of A after he rolls the ball for the first time. b. Find the speed of A after he catches the ball for the first time. c. Find the speed of A and B after the ball has made five round trips and is held by A . d. How many times can A roll the ball? e. Where is the centre of mass of the system A + B + ball at. the end of the nth trip?