Work and Energy
Multiple Choice Questions
1. When a body falls freely towards the earth, then its total energy
(a) increases
(b) decreases
(c) remains constant
(d) first increases and then decreases
Answer Answer is (c) remains constant Explanation : Body falling freely towards the earth possess same kinetic and potential energy and it follows Law of conservation of energy hence its total energy remains constant.Show Answer
(a) does not change
(b) becomes twice to that of initial
(c) becomes 4 times that of initial
(d) becomes 16 times that of initial
Answer Answer is (a) does not change Explanation: Potential energy is the product of height, mass and gravity. Hence height is a factor in determining potential energy. Here the height does not change hence potential energy of the car does not change.Show Answer
(a) $0^{0}$
(b) $45^{0}$
(c) $90^{\circ}$
(d) $180^{0}$
Answer Answer is (d ) $180^{\circ}$ Explanation: workdone $=FS \cos \Theta$ $Cos 180=-1$ Hence the answer is $180^{\circ}$Show Answer
(a) acceleration
(b) momenta
(c) potential energy
(d) kinetic energy
Answer Momentum, potential energy and kinetic energy varies with weight. But in this case acceleration is because of acceleration due to gravity which is independent of mass hence acceleration is the right answer.Show Answer
(a) $6 \times 103 J$
(b) $6 J$
(c) $0.6 J$
(d) zero
Answer Here Direction of workdone is perpendicular to gravitational force direction.Hence the workdone against the gravity is zero.Show Answer
(a) joule
(b) newton metre
(c) kilowatt
(d) kilowatt hour
Answer Answer is (c) kilowatt Explanation: Kilowatt is SI Unit of electrical powerShow Answer
(a) displacement
(b) force applied
(c) angle between force and displacement
(d) initial velocity of the object
Answer Answer is (d) initial velocity of the object Explanation: Workdone is the product of force and displacement hence force and displacement are the required attributes for the work to be done. But workdone is not dependent of initial velocity.Show Answer
(a) no energy
(b) electrical energy
(c) kinetic energy
(d) potential energy
Answer Answer is (d) potential energy Explanation: Potential energy is the energy stored in an object because of the position. Water in the dam possess energy because of position hence it is potential energy.Show Answer
(a) only potential energy
(b) only kinetic energy
(c) half potential and half kinetic energy
(d) more kinetic and less potential energy
Show Answer
Answer
Answer is (c) half potential and half kinetic energy
Explanation:
When body is at height h, its potential will be hundred percent and kinetic energy will be zero. In the same way when body reached ground its potential energy will be zero and kinetic energy will be maximum. At height h/2 both potential energy and kinetic energy of the body will be half.
Short Answer Questions
10. A rocket is moving up with a velocity $v$. If the velocity of this rocket is suddenly tripled, what will be the ratio of two kinetic energies?
Answer Initial velocity $=v=3 v$ Initial kinetic energy $=\dfrac{1}{2} v^{2}$ Kinetic energy $=\dfrac{1}{2} v^{2}$ $
\dfrac{1}{2} m(3 v)^{2}=9(\dfrac{1}{2} mv^{2})
$ Ratio between Initial kinetic energy and final kinetic energy is 1:9Show Answer
Answer $\mathbf{P}=f \times V$ $P_1=10 \times 8=80 W$ $P 2=25 \times 3=75 W$ Hence Avinash is more powerful than KapilShow Answer
Answer Total distance travelled by the boy $=1500 m+200 m+(1.5 \times 2 \pi r)$ Total distance travelled by the boy $=1500 m+200 m+(1.5 \times 2 \times 3.14 \times 100)=4442 m$ Frictional force $=5 N$ Workdone $=$ force $\times$ Displacement Workdone $=5 \times 4442=22210 J$Show Answer
Answer Momentum is the product of mass and velocity. If the body is at rest its velocity will be zero. If it is reast at height it possess gravitational potential energy hence mechanical energy.Show Answer
Answer No, Because its potential and kinetic energy are zero.Show Answer
Answer Power of pump $=2 kW=2000 W$ Time $(t)=60$ sec Height $(h)=10 m g=10 m / s 2$ Power =work done per unit time. Work done $=mgh=m \times 10 \times 10=100 m$ $2000 W=\dfrac{10 m}{60 s}$ Therefore, $m=1200 kg$ So, the pump can raise $1200 kg$ of water in one minute.Show Answer
Answer Person on Planet A can jump a height of $0.8 m$ because weight of person on plat A is half the weight that of earth. Hence acceleration due to gravity on planet A will also be half of that on earth.Show Answer
Answer $v^{2}-u^{2}=2$ as $s=\dfrac{v^{2}-u^{2}}{2 a}$ $F=ma$ $W=ma(\dfrac{.v^{2}-u^{2})}{2 a}.$ $=\dfrac{1}{2} mv^{2}-\dfrac{1}{2} mu^{2}$ $=(K . E) _{f}-(K . E) _{t}$Show Answer
Answer Force always acts in perpendicular to the displacement direction. If the object is moving in circular path then no work will be done despite of action of force.Show Answer
Answer $mgh=m \times 10 \times 10=100 m$ joules when $40 \%$ energy is reduced remaining energy will be 60 mjoules Hence $60-m \times 10 \times h$ $H=-6 m$Show Answer
Show Answer
Answer
Power of electric iron $=1200 W$
Usage per day $=30 min$
$ =30 / 60 hrs $
$ =0.5 hrs $
Number of days in the month of April=30days
Electrical energy consumed, E=Pxt 1200x0.5x30
$ \begin{aligned} & =18000 WH \\ & =18 KWH \\ & =18 \text{ units } \end{aligned} $
Therefore, The Total Electricity consumed in april month is 18 units
Long Answer Questions
21. A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy?
Answer Kinetic energy equation: $Ek_k=\dfrac{1}{2} mv2$ $
Ek=\dfrac{1}{2} mv 2
$ Momentum equation: $p=mv$ $
p=mv
$ Kinetic energy equation in terms of momentum: $Ek_k=\dfrac{p 2}{2 m}$ Kinetic energy of two objects will be same if their mass and momentum are same. Among light and heavy bodies Heavy body has highest momentum. When the momentum is equal light body has more kinetic energy.Show Answer
Answer $m(A)=m(B)=1000 kg$. $v=36 km / h=10 m / s$ Frictional force $=100 N$ car A moves with a uniform speed, which means engine of car applies a force equal to the frictional force Power $=$ Force $\times$ distance $/$ time $=F . V$ $
=100 N \times 10 m / s=1000 W
$ After collision $mA uA+mB uB=mA vA+mB v B$. $
\begin{aligned}
& 1000 \times 10+1000 \times 0 \\
& =1000 \times 0+1000 \times vB vB \\
& =10 m s-1
\end{aligned}
$Show Answer
Answer (a) Initial velocity of the trolley, $u=4 m / s$ Final velocity of the trolleyv $=0$ Mass of the trolleym $=5 kg$ Distance covered by the trolley before coming to rest, $s=16 m$ From Equation 2 as $=v 2-u 2$, $a=v 2-u 22 S$ $=0-(4) 22 \times 16$ $=0.5 m / s 2$ Force (frictional) acting on the trolley $=$ ma $
\begin{aligned}
& =40(-0.5) \\
& =-20 N \\
& =Fs=(20 N) \\
& =320 J
\end{aligned}
$ $
\text{ Work done on the trolley }=Fs=(20 N)(16 m)
$ (b) Since the girl does not move w.r.t. the trolley (as she is sitting on it),work done by the girl $=0$.Show Answer
(a) How much work is done by the men in lifting the box?
(b) How much work do they do in just holding it?
(c) Why do they get tired while holding it? ( $g=10 m s^{-2}$ )
Answer (a) $F=250 kg \times g=2500 N$ $S=1 m$ $W=F . s=250 Nm=2500 J$ (b) While holding box there is no displacement hence workdone is zero (c) While holding the box they apply muscular force which is equal and opposite to the gravitational force hence they feel tired while holding box.Show Answer
Answer Power is the rate of transfer of energy or rate of doing work. Watt is the unit of power and kilowatt is 1000 watts. $h=20 m$, and mass $=2000 \times 103 kg$ $=2 \times 106 kg$ Power $=m g h / t$ $=\dfrac{2 \times 106 \times 10 \times 20}{60}$ $w=\dfrac{4}{6} x 107 w=$ $\dfrac{2}{3} \times 107 w$Show Answer
Answer Power $=$ work/time work=force $x$ displacement force $=$ mass $x$ acceleration acceleration=velocity/time Therefore Power $=\dfrac{\text{ velocity } \times \text{ mass } \times \text{ displacement }}{time \times time}$ Here Power, $P=100 W$ velocity, $v=1 m / s$ since time, $t=1 s$ displacement, $s=1 m$ acceleration, $a=10 m / s$ From equation $P={m \times a \times s}$ $
\begin{gathered}
100=m \times 10 \\
m=10
\end{gathered}
$Show Answer
Answer Power of an object which does work at 1 Joules/sec is called watt 1 watt $=\dfrac{\text{ Joule }}{\text{ second }}$ 1 kilowatt= 1000 watts=1000J/sec mass of car $=150 kg$ power for each $kg=500 x$ 150=7500w speed $=20 m / s$ power=Force $x v$ $\therefore$ force $=$ power $/ v$ $\dfrac{7500}{20}$ $=3750 N$Show Answer
(i) a butterfly of mass $1.0 g$ that flies upward at a rate of $0.5 m s^{-1}$.
(ii) a $250 g$ squirrel climbing up on a tree at a rate of $0.5 m s^{-1}$.
Show Answer
Answer
i) Butterfly force $=m g=1 / 100$ power $=f \times s \div t$. $\{s \div t=$ velocity $\}$ power $=1 \div 100 \times .5$ power $=1 \div 200 W$
ii) squirrel force $=mg=25$
power=25×.5
power $=12.5 W$
