A small steel sphere of mass m is falling ver | vedclass

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

Question

(A) Since the sphere is falling with a constant speed $v$,the kinetic energy $KE = \frac{1}{2} mv^2$ remains constant over time. Therefore,the rate of

Vedclass · Accepted Answer

constant and equal to $\frac{1}{2} mv^2$ || decreases at a rate of $mgv$

Vedclass · Answer

(A) Since the sphere is falling with a constant speed $v$,the kinetic energy $KE = \frac{1}{2} mv^2$ remains constant over time. Therefore,the rate of change of kinetic energy is $0$.The gravitational potential energy $PE$ is given by $PE = mgh$. As the sphere falls,its height $h$ decreases with time. The rate of change of potential energy is $\frac{d(PE)}{dt} = mg \frac{dh}{dt}$.Since the sphere is moving downwards with a constant speed $v$,the rate of change of height is $\frac{dh}{dt} = -v$. Thus,the rate of change of potential energy is $-mgv$. This indicates that the gravitational potential energy decreases at a rate of $mgv$.

$A$ small steel sphere of mass $m$ is falling vertically through a viscous liquid with a constant speed $v$. Which row in the table correctly describes the changes with time in the kinetic energy and gravitational potential energy of the sphere?

Similar Questions

Eight equal drops of water are falling through air with a steady velocity of $10 \,cm \,s^{-1}$. If the drops combine to form a single drop, then the terminal velocity of this big drop is:

Why do dust particles settle down on the floor in a closed room? Explain.

$A$ liquid drop of mass $m$ and radius $r$ is falling from a great height. Its terminal velocity is proportional to ............

Eight equal drops of water,each of radius $r = 2 \ mm$,are falling through air with a terminal velocity of $16 \ cm/s$. The eight drops combine to form a single big drop. The terminal velocity of the bigger drop will be $.... \ cm/s$.

$A$ small ball of mass $M$,radius $R$ and density $\rho$ moves with terminal velocity through a container filled with glycerine of density $\sigma$. The viscous force acting on the ball is ($g=$ gravitational acceleration).

Vedclass Test Series

Exam Paper Generator

Online Exam Module