Tag: work, energy and power

Questions Related to work, energy and power

A machine gun fires 360 bullets per minute. Each bullet moves with a  velocity of 600 ms$^{-1}$. If the power of the gun is 5.4 kw, the mass of each bullet is,

power work and power work, energy and power physics energy and its forms

  1. 5 kg

  2. 0.5 kg

  3. 0.05 kg

  4. 5 gm

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Correct Option: D
Explanation:

Given,

Number of bullets, $n=360\,nos.$

Mass of bullet, $m$

Power, $=5400watt$

Kinetic energy of 360 bullets, $K.E=n\times \dfrac{1}{2}m{{v}^{2}}=360\times \dfrac{1}{2}\times m\times {{600}^{2}}=648\times {{10}^{5}}m\,\,J$

$ Power=\dfrac{kineticenergy}{time} $

$ 5400=\dfrac{648\times {{10}^{5}}m}{60} $

$ m=5\times {{10}^{-3\,}}kg\,=\,5\,gram\, $

Hence, weight of each bullet is $5\,gram$

The driving side belt has a tension of $1600\ N$ and the slack side has $500\ N$ tension. The belt turns a pulley $40\ cm$ in radius at a rate of $300\ rpm$. The pulley drives a dynamic having $90\%$ efficiency. How many kilowatt are being delivered by the dynamo?

power work and power work, energy and power physics energy and its forms

  1. $12.4\ kW$

  2. $6.2\ kW$

  3. $24.8\ kW$

  4. $13.77\ kW$

Show answer
Correct Option: A

A heating unit on an electric stove is rated at $880  W$. It is connected to a power supply of $220  V$. The current it will consume is

power work and power work, energy and power physics energy and its forms

  1. 2 amp

  2. 4 amp

  3. 6 amp

  4. 8 amp

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Correct Option: B
Explanation:

Power $= V \times I$
or, $880 = 220 \times I$
or, $I = \displaystyle\frac{880}{220} = 4  amp$.

The average power required to lift a $100kg$ mass through a height of $50$ metres in approximately $50$ seconds would be ( in J/s)

power work and power work, energy and power physics energy and its forms

  1. $50$

  2. $5000$

  3. $100$

  4. $980$

Show answer
Correct Option: D
Explanation:

$Power= Work/Time= F.s/t=mgs/t=(100\times 9.8\times 50)/50= 980W $


Hence correct answer is option $D $ 

A tap supplies water at 22C. A man takes 11 litre water per minute at 37C from the geyser. The power of geyser is

power work and power work, energy and power physics energy and its forms

  1. 525 W

  2. 1050 W

  3. 1575 W

  4. 2100 W

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Correct Option: B

A rectangular block of dimensions $6m\times 4m\times 2m$ and of density $1.5\ gm/c.c$ is lying on horizontal ground with the face of large area in contact with the ground. The work done in arranging it which its smallest area in contact with a ground is, $(g=10ms^{-1})$

power work and power work, energy and power physics energy and its forms

  1. $2880\ kJ$

  2. $1440\ kJ$

  3. $3800\ kJ$

  4. $720\ kJ$

Show answer
Correct Option: B
Explanation:

m=v*density

m=$6\times 4\times 2\times 1.5\times 10^3=72\times 10^3$kg
when face with large area is in contact with the ground its height is 2m
Centre of mass is at a height of 1m

when face with small area is in contact with the ground its height is 6m
Centre of mass is at a height of 3m
W=$72\times 10^4(3-1)=1440 kJ$

A small body of mass $m$ is located on a horizontal plane. The body acquires a horizontal velocity ${v} _{0}$. Find mean power developed by the frictional force, during the whole time of its motion. Coefficient of friction is $\mu$

power work and power work, energy and power physics energy and its forms

  1. $\cfrac { -\mu mg{ v } _{ 0 } }{ 3 } $

  2. $\cfrac { -\mu mg{ v } _{ 0 } }{ 2 } $

  3. $\cfrac { -\mu mg{ v } _{ 0 } }{ 5 } $

  4. $\cfrac { -\mu mg{ v } _{ 0 } }{ 6 } $

Show answer
Correct Option: B

A body of mass $10kg$ is moving along positive $x-$axis with $5\ m/s$ at $t=0$ and is moving along negative $x-$axis with same speed at $t=10\ s$. Average power of the force acting on the body is:

power work and power work, energy and power physics energy and its forms

  1. $Zero$

  2. $25\ W$

  3. $50\ W$

  4. $100\ W$

Show answer
Correct Option: A
Explanation:

since there is no acceleration 

there is no power
P=0

A light bulb has the rating 100 W, 220 V. If the supply voltage is 110 V, then power consumed by the bulb is

power work and power work, energy and power physics energy and its forms

  1. 50 W

  2. 75 W

  3. 25 W

  4. 20 W

Show answer
Correct Option: C
Explanation:
$P =\dfrac{ V^2}R$  

If $V = 220$ V we have

$100 W =\dfrac{ 220^2}R$

$R = \dfrac{220^2}{100} Ω = 484 Ω$. This is the resistance of the bulb.

When $V = 110$ V, power consumed $=\dfrac{V^2}R= \dfrac{110^2}{484} = 25$ W.

So, 25 W power is consumed when it is operated on 110 V.


A force $\vec {F}=(3\hat {i}+4\hat {j})N$ acts on $2kg$ movable object that moves from an initial position $\vec {r} _{1}=(-3\hat {i}-2\hat {j})m$ to a final position $\vec {r} _{1}=(5\hat {i}+4\hat {j})m$ in $6s$. The average power delivered by the force during the interval of $6s$ is equal to :

power work and power work, energy and power physics energy and its forms

  1. $8\ watt$

  2. $\dfrac{50}{6}\ watt$

  3. $15\ watt$

  4. $\dfrac{50}{3}\ watt$

Show answer
Correct Option: A
Explanation:

 

Given,

Force, $\vec {F}=(3\hat {i}+4\hat {j})N$

Displacement, $\vec{d}={{\vec{r}} _{2}}-{{\vec{r}} _{1}}=(5\hat{i}+4\hat{j})-(-3\hat{i}-2\hat{j})=\left( 8\hat{i}+6\hat{j} \right)\,m$

Work, $W=\vec{F}.\vec{d}=\left( 3\hat{i}+4\hat{j} \right)\left( 8\hat{i}+6\hat{j} \right)=48\,J$

Average power $P=\dfrac{W}{t}=\dfrac{48}{6}=8\,W$

Average power is $8\,W$