A ball is thrown on a lawn in such a way that | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the mass of the ball be $m$ and its radius be $R$. The moment of inertia of a solid sphere about its center is $I = \frac{2}{5} mR^2$.Initiall

Vedclass · Accepted Answer

$\frac{5}{7} v_0$

Vedclass · Answer

(C) Let the mass of the ball be $m$ and its radius be $R$. The moment of inertia of a solid sphere about its center is $I = \frac{2}{5} mR^2$.Initially,the ball has linear velocity $v_0$ and zero angular velocity.As the ball slides,friction acts on it,creating a torque that increases its angular velocity until it starts rolling without slipping.During this process,the angular momentum about the point of contact on the ground remains conserved because the torque due to friction about this point is zero.Initial angular momentum about the point of contact: $L_i = m v_0 R$.Final angular momentum about the point of contact when rolling without slipping occurs (where $v = \omega R$): $L_f = I_{cm} \omega + m v R = (\frac{2}{5} mR^2) (\frac{v}{R}) + m v R = \frac{2}{5} m v R + m v R = \frac{7}{5} m v R$.Equating $L_i = L_f$: $m v_0 R = \frac{7}{5} m v R$.Solving for $v$: $v = \frac{5}{7} v_0$.

$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.

Similar Questions

Percentage of gold in $14$ carat gold is (in $\%$)

The cubic unit cell of a metal (molar mass $= 63.55 \ g \ mol^{-1}$) has an edge length of $362 \ pm$. Its density is $8.92 \ g \ cm^{-3}$. The type of unit cell is

Which of the following is a bacterial domain?

Smoke is an example of ...

Vedclass Test Series

Exam Paper Generator

Online Exam Module