Tag: work and power

Questions Related to work and power

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

  1. 2 amp

  2. 4 amp

  3. 6 amp

  4. 8 amp


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)

  1. $50$

  2. $5000$

  3. $100$

  4. $980$


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

  1. 525 W

  2. 1050 W

  3. 1575 W

  4. 2100 W


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, $(g=10ms^{-1})$

  1. $2880\ kJ$

  2. $1440\ kJ$

  3. $3800\ kJ$

  4. $720\ kJ$


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 $\mu$

  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 } $


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:

  1. $Zero$

  2. $25\ W$

  3. $50\ W$

  4. $100\ W$


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

  1. 50 W

  2. 75 W

  3. 25 W

  4. 20 W


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 :

  1. $8\ watt$

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

  3. $15\ watt$

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


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 $8\,W$ 

A weight lifter lifts $300\ kg$ from the ground to a height of $2$ meter in $3$ seconds. The average power generated by him is:-

  1. $5880\ watt$

  2. $4410\ watt$

  3. $2205\ watt$

  4. $1960\ watt$


Correct Option: D

Human heart pumps $70\ cc$ of blood at each beat against a pressure of $125\ mm$ of $Hg$. If the pulse frequency is $72$ per minute, the power of the heat is nearly.

  1. $1.2\ W$

  2. $1.4\ W$

  3. $1.6\ W$

  4. $1.8\ W$


Correct Option: B