A solid sphere of mass m rolls without slippi | vedclass

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

Question

(D) The total kinetic energy of a rolling solid sphere is the sum of its translational kinetic energy and rotational kinetic energy.Total kinetic ener

Vedclass · Accepted Answer

$v\sqrt {\frac{{7m}}{{5k}}} $

Vedclass · Answer

(D) The total kinetic energy of a rolling solid sphere is the sum of its translational kinetic energy and rotational kinetic energy.Total kinetic energy $K = K_{trans} + K_{rot} = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$.For a solid sphere,the moment of inertia $I = \frac{2}{5}mr^2$ and for rolling without slipping,$\omega = \frac{v}{r}$.Substituting these values,$K = \frac{1}{2}mv^2 + \frac{1}{2}(\frac{2}{5}mr^2)(\frac{v}{r})^2 = \frac{1}{2}mv^2 + \frac{1}{5}mv^2 = \frac{7}{10}mv^2$.By the law of conservation of energy,this kinetic energy is converted into the potential energy of the spring at maximum compression $x$.$\frac{7}{10}mv^2 = \frac{1}{2}kx^2$.Solving for $x$,$x^2 = \frac{14mv^2}{10k} = \frac{7mv^2}{5k}$.Therefore,$x = v\sqrt{\frac{7m}{5k}}$.

$A$ solid sphere of mass $m$ rolls without slipping with velocity $v$ and compresses a spring of spring constant $k$ as shown in the figure. The maximum compression in the spring will be:

Similar Questions

Molten sodium chloride conducts electricity due to the presence of

$A$ body is projected from the ground at an angle of $\tan ^{-1}(\sqrt{7})$ with the horizontal. At half of the maximum height, the speed of the body is '$n$' times the speed of projection. The value of '$n$' is

Data Entry - Physics

Which of the following organs is known as the 'blood bank' of the human body?

$15 \text{ mL}$ of aqueous solution of $Fe^{2+}$ in acidic medium completely reacted with $20 \text{ mL}$ of $0.03 \text{ M}$ aqueous $Cr_2O_7^{2-}$. The molarity of the $Fe^{2+}$ solution is $.......... \times 10^{-2} \text{ M}$ (Round off to the Nearest Integer).

Vedclass Test Series

Exam Paper Generator

Online Exam Module