Q39 of 42 Page 35

A cricket bowler releases the ball in two different ways

(a) giving it only horizontal velocity, and


(b) giving it horizontal velocity and a small downward velocity. The speed vs at the time of release is the same. Both are released at a height H from the ground. Which one will have greater speed when the ball hits the ground? Neglect air resistance.


In case (a), we have only horizontal velocity. From the conservation of energy at the point when ball hits the ground,

K.E = P.E




For case 2 we also have an additional downward velocity vs in addition to horizontal velocity vh.

So, the total velocity is



At the point of contact, vh= 0


So, from the conservation of energy,




Hence, both techniques will yield the same speed.


More from this chapter

All 42 →
37

A racing car travels on a track (without banking) ABCDEFA (Fig. 5.10). ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 m s-1. Find the minimum time for completing one round.


 38

The displacement vector of a particle of mass m is given by r (t) = î A cos ωt + ĵ B sin ωt.

(a) Show that the trajectory is an ellipse.


(b) Show that F = −mω2r


 40

There are four forces acting at a point P produced by strings as shown in Fig. 5.11, which is at rest. Find the forces F1 and F2 .

.


41

A rectangular box lies on a rough inclined surface. The co-efficient of friction between the surface and the box is μ. Let the mass of the box be m.

(a) At what angle of inclination θ of the plane to the horizontal will the box just start to slide down the plane?


(b) What is the force acting on the box down the plane, if the angle of inclination of the plane is increased to α θ >?


(c) What is the force needed to be applied upwards along the plane to make the box either remain stationary or just move up with uniform speed?


(d) What is the force needed to be applied upwards along the plane to make the box move up the plane with acceleration


a?