Q. The figure-$3.71 $ shows the variation of energy with the orbit radius of a body in circular planetary motion. Find the correct statement about the curves $A, B$ and $C$ :

Work, Energy and Power Report Error

A

$A$ shows the kinetic energy, $B$ the total energy and $C$ the potential energy of the system.

B

$C$ shows the total energy, $B$ the kinetic energy and $A$ the potential energy of the system.

C

$C$ and $A$ are kinetic and potential energies respectively and $B$ is the total energy of the system.

D

$A$ and $B$ are kinetic and potential energies and $C$ is the total energy of the system.

Solution:

For a planetary motion of body being a bounded motion its total energy and potential energy must be negative with respect to zero energy at infinite separation from the center of force. So among the given option (D) is correct.

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3. A body constrained to move along Z-axis of a coordinate system is subjected to a constant force $F$ given by $F =-\hat{i ⁡}+2\hat{j ⁡}+3\hat{k}N⁡$ where $\hat{i}$ , $\hat{j}$ and $\hat{k}$ are the unit vector along the X, Y and Z-axis of the system respectively. What is the work done by this force in moving the body a distance of $4 \, m$ along the Z-axis?

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4. A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_{c}$ is varying with time $t$ as $a_{c}=k^{2} \, rt^{2}$ , where $k$ is a constant. The power delivered to the particle by the force acting on it is

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5. A particle is released from a height $h$ , At a certain height; its kinetic enegy is two times its potential energy. Height and speed of the particle at that instant are

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Q. The figure-$3.71 $ shows the variation of energy with the orbit radius of a body in circular planetary motion. Find the correct statement about the curves $A, B$ and $C$ :

$A$ shows the kinetic energy, $B$ the total energy and $C$ the potential energy of the system.

$C$ shows the total energy, $B$ the kinetic energy and $A$ the potential energy of the system.

$C$ and $A$ are kinetic and potential energies respectively and $B$ is the total energy of the system.

$A$ and $B$ are kinetic and potential energies and $C$ is the total energy of the system.

For a planetary motion of body being a bounded motion its total energy and potential energy must be negative with respect to zero energy at infinite separation from the center of force. So among the given option (D) is correct.

Questions from Work, Energy and Power

1. Identify the false statement from the following

2. The machine gun fires $240 \, $ bullets per minute. If the mass of each bullet is $10 \, g$ and the velocity of the bullets is $600 \, m \, s^{- 1}$ ,the power (in $kW$ )of the gun is

4. A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_{c}$ is varying with time $t$ as $a_{c}=k^{2} \, rt^{2}$ , where $k$ is a constant. The power delivered to the particle by the force acting on it is

5. A particle is released from a height $h$ , At a certain height; its kinetic enegy is two times its potential energy. Height and speed of the particle at that instant are

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1. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

2. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

3. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

5. Calculate the acceleration of the block and trolly system shown in the figure The coefficient of kinetic friction between the trolly and the surface is $0.05. (g = 10 \,m/s^{2}$, mass of the string is negligible and no other friction exists

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