A solid sphere of radius R is lying on a horizontal smooth surface. The sphere is hit by stick held horizontally at a height of $\frac{R}{2}$ above the center. The sphere moves forward with a velocity $v_{0}$ and angular velocity $ω_{0}$ about its center. Then $ω_{0}$ =

Q. A billiard ball initially at rest is given an impulse by a cue as shown in figure. The cue is held horizontal at a distance

h

above the centre line. The ball leaves the cue with speed

v_{o}

and acquires a final velocity

\frac{9 v_{o}}{7}

. What is the value of

h

in terms of the radius of ball?

A billiard ball (of radius R), initially at rest is given a harp impulse by a cue. The cue is held horizontally a distance h above the central line. The ball leaves the cue with a speed $V_{0}$ , eventually acquires a final speed of $\frac{9}{7} V_{0}$ . Find h.

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A billiard ball of mass m and radius r, when hit in a horizontal direction by a cue at a height h above its centre, acquired a linear velocity v0. The angular velocity ω0 acquired by the ball is

The correct option is C 5v0h2r2The effect of force F lies at high h.Torque τ=IαF⋅h=25mr2⋅ωt [∵α=ωt]m⋅ah=25mr2ωtm⋅v0th=25mr2ωtω=5v0h2r2

A billiard ball of mass $m$ and radius $r$ , when hit in a horizontal direction by a cue at a height $h$ above its centre, acquired a linear velocity $v_{0}$ . The angular velocity $ω_{0}$ acquired by the ball is