Work Energy and Power Test

Result

Work Energy and Power Test - 52

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Weekly Quiz Competition

Question 1
1 / -0

A force $$F=Ay^{2}+By+C$$ acts on a body in the $$y$$ direction, The work done by this force during a displacement from $$y=-a$$ to $$y=a$$ is

A
$$\dfrac{2Aa^{2}}{3}$$

B
$$\dfrac{2Aa^{2}}{3}+2Ca$$

C
$$\dfrac{2Aa^{2}}{3}+\dfrac{Ba^{2}}{2}+Ca$$

D
$$None\ of\ these$$

Solution
Question 2
1 / -0

Gravel is dropped on a conveyor belt at the rate of $$2kg/s$$. The extra force required to keep the belt moving at $$3 ms^{-1}$$ is

A
$$1 N$$

B
$$3 N$$

C
$$4N$$

D
$$6 N$$

Solution
Question 3
1 / -0

A ball of mass $$5$$ kg experiences a force $$F=2x^{2}+x$$. Work done in displacing the ball by $$2$$ m is

A
$$22/3$$ J

B
$$44/3$$ J

C
$$32/3$$ J

D
$$16/3$$ J

Solution
Question 4
1 / -0

A body of mass 0.5 kg travels in a straight line with velocity $$v=ax^{3/2}$$ where $$a=5m^{-1/2}s^{-1}$$. the work done by the net force during its displacement from $$x=0$$ to $$x=2m$$ is

A
$$1.5J$$

B
$$50J$$

C
$$10J$$

D
$$100J$$

Solution
Question 5
1 / -0

A car is travelling at 5 m/s up a gradient of 1 in 20. The car weight 6 tonnes and the friction is 48 kg wt. The work done per second in maintaining the motion of car up the gradient is $$(g=10ms^{-2}$$)

A
12400 W

B
1362 W

C
17400 W

D
1520 W

Solution
Question 6
1 / -0

A force acts on a $$20g$$ particle in such a way that the position of the particle as a function of time is given by $$x=3t-4t^2+t^3$$, where x is in meters and $$t$$ is in seconds. The work done during the first $$4sec$$ is:

A
$$-1.6J$$

B
$$-1600J$$

C
$$2.6 J$$

D
$$1600J$$

Solution

Mass $$\left(m\right) =20gm=0.020kg$$
$$x=3t-4t^2+t^3m$$
$$\Rightarrow v=\dfrac{dx}{dt}=3-8t+3t^2m/s$$
$$\Rightarrow a=\dfrac{dv}{dt}=-8+6tm/s^2$$
Force $$=ma=0.120t-0.160N$$
Work done $$=dw=Fdx=F\times \left( \dfrac{dx}{dt}\right)\times dt$$
$$\Rightarrow dw=\left( 0.120+0.160\right) \times \left( 3-8t+3t^2\right)dt$$
$$=0.360t^3-1.440t^2+1.640t-0.450$$
$$\Rightarrow w=integral\;of\;dw\;from\;\;\;\;t=0\;to\;4\;sec$$
$$=\left[ 0.090t^4-0.490t^3+0.82t^2-0.450t\right],t=0\;to\;4\;s$$
$$=2.88J.$$
Hence, the answer is $$2.88J.$$
Question 7
1 / -0

If a resultant force of $$30N$$ acts on a body of mass $$6kg$$.What is the acceleration of the body?

A
$$20m/sec^2$$

B
$$12m/sec^2$$

C
$$5m/sec^2$$

D
$$8m/sec^2$$

Solution
Question 8
1 / -0

A force of $$F = 2x\hat{i} + 2\hat{j} + 3z^{2}\hat{k} N$$ is acting on a particle. Find the work done by this force in displacing the body from (1,2,3) into (3,6,1) m.

A
$$-10 J$$

B
$$100$$

C
$$10 J$$

D
$$1 J$$

Solution
Question 9
1 / -0

Two wires of the same diameter of the same material having the length $$\ell$$ and $$2\ell$$. If the force is applied on each, the ratio of the work done in the two will be

A
$$1: 2$$

B
$$1: 4$$

C
$$2: 1$$

D
$$1: 1$$

Solution

$$\begin{array}{l} W=\dfrac { 1 }{ 2 } Fl\, \, \, \, \, \, \, \, \, \, \, \left( { W\, \alpha \, l } \right) \\ \dfrac { { { W_{ 1 } } } }{ { { W_{ 2 } } } } =\dfrac { { { l_{ 1 } } } }{ { { l_{ 2 } } } } =\dfrac { l }{ { 2l } } =\dfrac { 1 }{ 2 } =1:2 \end{array}$$
Hence,
option $$(A)$$ is correct answer.
Question 10
1 / -0

A particle of mass 1 kg is projected under gravity at an angle $${ 37 }^{ o }$$ with horizontal with 50 m/s. Instantaneous power delivered by gravity at t=1s is $$\left( sin{ 37 }^{ o }=\frac { 3 }{ 5 } ,cos{ 37 }^{ o }=\frac { 4 }{ 5 } \right) $$

A
200 J/s

B
-200 J/s

C
Zero

D
-400 J/s

Solution