Science M.C.Q. [1 M]

Prefix Mega means $10^6$.
So, $1$ Megawatt = $1 \times 10^6 \mathrm{~W}$

Energy is defined as the ability to do work and its $SI$ unit is Joule.

Work = Force $\times $ Displacement
Here, the wall is not moving although the boy is pushing hard.
$\therefore$ Displacement $= 0$
$\therefore$ Work $= 0$

kinetic energy is energy possessed by body due to virtue of its motion.
only boy in option $A$ is in motion so only he has some kinetic energy.
rest option have things at rest so no kinetic energy.

Weight of the girl $(W) = 400N$
Vertical height $(h) = 2m$
Acceleration due to gravity $(g) = 10m/s^2$
We can calculate the work done against gravity in moving a body of mass $(m)$ by a height $(h)$ as,
Work done in lifting a body $= ($Weight of body$)($Vertical distance$)$
So,
$W = (m)(g)(h)$
So,
Work done in lifting a body
$= (400)(2)J$
$= 800J$

 The commercial unit of electrical energy is Kilowatt $−$ hour (kWh).
$1\ kWh$ is equal to $1$ unit of energy.

 Kinetic energy is the energy possessed by the body by virtue of its motion and potential energy is the energy possessed by the virtue of its position and shape. Energy is required to do work.
Hence work, kinetic energy, potential energy all can be measured using same unit, i.e joule.
So, force is the physical quantity here which is different from others as given by product of mass and acceleration. $S.I$ unit of force is $N ($newton$).$

 In this case, the force of gravity is acting in the downward direction. But, the displacement of the body is in the upward direction. Since the angle between the force and displacement is $180^{\circ}$, the work done by the gravitational force on the body is negative.

 Law of conservation of energy states that the energy can neither be created nor destroyed but can be transformed from one form to another. Let us now prove that the above law holds good in the case of a freely falling body. Total energy at $A =$ Potential energy $+$ Kinetic energy.

Energy is the capacity of a physical system to perform work. Energy exists in several forms such as heat energy, kinetic or mechanical energy, light energy, potential energy, electrical energy, or other forms. According to the law of conservation of energy the total energy of a system remains constant, though energy may transform into another form.
The SI unit of energy is the joule $(J)$ or newton-meter $(N-m).$ Joule is also the SI unit of work.

We know that potential energy is the energy possesd by the virtue of its position.
So, $F =$ mgh
Where, $m =$ mass
So, From above equation we can deduce that potential energy depends on the mass of the substance.

Practical unit of power is horse power $(hp).$
$1\ hp = 746W ,$ where $W$ is Watt $($the $SI$ unit of power$).$

The watt - hour $(Wh)$ is a unit of electric energy equivalent to one watt $(1\ W)$ of power expended for one hour $(1\ h)$ of time. Watt-hour is commonly used in electrical applications.
$1\ Wh = 1 × 60 × 60 = 3600J$

$\text{P}=\frac{\text{w}}{\text{t}}$
$=\frac{\text{F}\times\text{d}}{\text{t}}=\text{m}\times\text{a}\times\text{v}$
$=500\times9.8\times0.2$
$=980\text{ Watt}$
$1\ H.P. = 746$ watt
$1.3$ horse power

 A body at rest can have potential energy because $PE$ is due to position of object but it does not have kinetic energy because $KE$ is due to motion but object is at rest so no $KE$ will be present.Momentum is also not present because momentum is due to velocity and velocity is zero in this case.
For example an object at a roof at rest have no $KE$ but it has gravitational potential energy due to it's height above ground given by mgh.

 A body of mass $20\ kg$ is held at a height of $2m$ above the ground means there is no displacement because of which there is no change in its potential energy. Hence work done is zero.

Potential energy =$ mgh$
$m →$ mass
$g →$ acceleration due to gravity
$h →$ height from ground
$P.E.$ is directly proportional to the height from the ground.
Hence a student sitting at the top of a tree has more potential energy than the student who is sitting on the ground.

Power, $(P) = 100W$
Time duration, $(t) = 60s$
Now, we can calculate the electrical energy consumed as,
Energy consumed $= ($Power$)($Time$)$
So,
Energy consumed
$= (100)(60)J$
$= 6000J$
So, the energy consumed is $6000 J.$

$90\%$ the of the energy is used to turn the turbine.
$\Rightarrow $ So the power generated in the turbine is $= 0.9 \times ($change in $PE$ of the water per second$)$
$\Rightarrow 0.9 \times 15 \times 10 \times 60$
$= 8100$ watt.

Given,
Power $= 10^7 \mathrm{KW}$
$=\frac{\text{Energy}}{\text{Time}}$
Energy = $\left(10^7 \times 10^3\right) \times(24 \times 3600)$
$= 864 \times 10^{12}$ Joule
$E = \mathrm{mc}^2$
Have, $c =$ Speed og light
$=3 \times 10^8 \mathrm{~m} / \mathrm{s}$
$\text{m}=\frac{864\times10^{12}}{9\times10^{16}}$
$\text{m}=96\times10^{-4}$
$\text{m}=96\times10^{-3}\text{kg}$
$=9.6\text{gm}$

 $\xrightarrow{5\text{N}}15\text{kg}$
$\text{a}=\frac{5\text{N}}{15\text{kg}}=\frac{1}{3}\text{m/ s}^2$
$\text{S}=\text{vt}+\frac{1}{2}\text{at}^2\ [\text{t}=1\text{sec}]$
$\text{S}=\frac{1}{2}\times\frac{1}{3}\times(1)^2$
$=\frac{1}{6}$
$\text{W}=\text{F}\times\text{S}$
$\frac{5}{6}\text{J}$

$\text{power}=\frac{\text{energy}}{\text{time}}$
$1.2=\frac{\text{energy}}{18000}$
energy required $= 21600J$
Total time required for $21600J$ is $\frac{21600}{1.6}=13500$

$CGS$ unit of energy is Dyne−cm which is also known as erg.

In $SI$ unit energy is measured in Joules.
Therefore, $S.I$ unit of potential energy is Joule$(J).$

Work done by brakes $(F × d)$ transfers their $KE.$
$(\text{F}\times\text{d})=\frac{1}{2}\text{mv}^2$
Since both have same $KE$ and both subject to same force $(F).$
then distances $(d)$ are equal.

One unit of household is $1\ kwh$
kwh $=$ kilo watt hour
$1$ unit $= 1\ kWh$
$⇒ 1$ unit $= 10^3 \mathrm{~W} \times 3600 \mathrm{~s}$
$⇒ 1$ unit $= 3.6 \times 10^6 \mathrm{~J}$

A raised hammer possesses $P.E$ Energy possessed by a body by virtue of its position is called as potential energy. Similarly is the case when a hammer is raised. A raised hammer possesses potential energy by virtue of its height above ground level.

$\text{Power}=\frac{\text{Work done}}{\text{time}}$
$=\frac{\frac{1}{2}\text{m}(\text{v}^2-\text{u}^2)}{\text{t}}$
$\text{P}=\frac{1}{2}\times\frac{2.05\times10^6\times\big[(25)^2-(5^2)\big]}{\text{t}}$
$\text{P}=2.05\times{10^6}\text{W}$
$=2.05\text{MW}$

The kilowatt-hour is a unit of energy equal to $1,000$ watt-hours, or $3.6$ mega-joules. If the energy is being transmitted or used at a constant rate (power) over a period of time, the total energy in kilowatt-hours is the product of the power in kilowatts and the time in hours. The kilowatt-hour is commonly used as a billing unit for energy delivered to consumers by electric utilities.

Since the ball is in free-fall, the only force acting on it is gravity. Therefore, we can use the principle of conservation of mechanical energy - initially the ball has potential energy and no kinetic energy. As it falls, its total energy (the sum of the $KE$ and the $PE)$ remains constant and equal to its initial $PE.$ when reaches the ground there is no $PE$ only $KE\ I.E.,$ Equal to initial $PE$

Potential energy is the energy possessed by a body by the virtue of its height from the ground and in the given case, the car only increases its velocity $4$ times but its height from the ground remains constant. Thus, the potential energy does not change.

Mass of the load ($m$$_1$) $= 0.2\ kg$
Height $(h) = 3\ m$
Acceleration due to gravity $(g) = 10\ m/s$$^2$
Time taken $(t) = 2\ s$
We can calculate the work done against gravity as,
Work done by the car = (Weight of body)(Vertical distance)
$= (0.2)(10)(3)J$
$= 6J$
Now, we can calculate the power of the boy as,
$\text{Power}=\frac{\text{Work done}}{\text{Time}}$
So,
$\text{Power}=\frac{6}{2}\text{W}$
$=3\text{W}$
So, the power is $3W$.

1. Work done $W = F.d \cos\theta$

2. We know that work done, $W = F.d \cos\theta$

3. We know that work done, $W = d \cos\theta$

4. Work done at $\theta=180^\circ,\ \text{W}=\text{F.d}\ \cos\theta\ (\therefore\cos180^\circ=-1)$

Mass of the bullet, $(m), = 0.02\ gm$
Momentum of the bullet, $(P) = 10\ kg.m/s$
The relation between momentum, mass and kinetic energy is as follows:
$\text{K.E.}=\frac{1}{2}\Big(\frac{\text{p}^2}{\text{m}}\Big)$
So,
$\text{K.E.}=\frac{1}{2}\Big(\frac{(10)^2}{0.02}\Big)\text{J}$
$=\frac{100}{0.04}\text{J}$
$=2500\text{J}$
$2.5\text{KJ}$

$\text{F}=\text{kx}\ þ\ \text{x}$
$=\frac{\text{F}}{\text{k}}=\frac{\text{mg}}{\text{k}}$
$=\frac{20\times9.8}{4000}$
$=4.9\text{cm}$

We know that , $P.E =$ mgh So, It is directly proportional to height and mass.
Since both the weights are at the same height, so the weight with a larger mass will have more potential energy.
Since 10kg object has a larger mass than a $5\ kg,$ so, the potential energy of a $10\ kg$ mass will be greater.

1. The acceleration for the entire journey of the stone is constant, as acceleration due to gravity near the surface of the earth is constant.
2. The velocity of the stone at $P$ will be the least. Hence, kinetic energy at this point will be the least.
3. The stone is at a maximum height at point $P.$ Hence, the potential energy is the maximum at $P.$
4. Weight of the stone will remain nearly constant, as acceleration due to gravity near the surface of the earth is constant.

Momentum, potential energy and kinetic energy depend on the mass of the object; as well as on some other factors. But acceleration, in this case, is the acceleration due to gravity; which does not depend on mass or velocity. So, options $(a)$ is correct.

The energy stored in food is measured in kilo calories. This is the unit of energy in food.
Where $1$ kilo calorie $= 4184$ Joules

Electricity bill is measured in units where $1$ unit is equal to kWh which is the unit of energy. Hence, when we pay for our electricity bill, we pay for the amount of electrical energy consumed by us.

A ball rolling down a hill has both Kinetic and potential energy. Kinetic energy is due to motion. So if the ball is rolling down it has kinetic energy. Potential energy is the stored energy which is waiting to be used. If the ball is at a greater height it will have more potential energy. So when the body starts rolling the stored potential energy gets converted into kinetic energy which causes its motion. Hence a body rolling down a hill has both $K.E$ and $P.E$

Unit of force is Newton $(N).$

Practical unit of power is horsepower $(hp).$
One horsepower is equal to $746$ watts.
whereas Watt is the SI unit of power.

power is the rate of doing work. It is equivalent to an amount of energy consumed per unit time. In the $SI$ system, the unit of power is the joule per second $(J/s).$

First find out force
force $=$ mass $×$ acceleration
force $= 3 × 10$
force $= 30N$
work $=$ force $×$ displacement
work $= 30 × 200$
work $= 6000$ Joule
$= 6 \times 10^3 \mathrm{~J}$

$W = F.S$
As work done is independent of time. So, both the man does same work.
Hence, the work done on the body against gravitation are in ratio $1 : 1.$