Work and Energy Test

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Work and Energy Test - 45

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Weekly Quiz Competition

Question 1
1 / -0

A block of mass $$10kg$$ accelerates uniformly from rest to a speed of $$2m/s$$ in $$20$$ sec. The average power developed in time interval of $$0$$ to $$20$$ sec is

A
$$10W$$

B
$$1W$$

C
$$20W$$

D
$$2W$$

Solution
Question 2
1 / -0

Which of the following statements is incorrect?

A
No work is done if the displacement is perpendicular to the direction of the applied force

B
If the angle between the force and displacement vectors is obtuse, then the work done is negative

C
Frictional force is a non-conservative

D
All the central forces are non-conservative

Solution

Non-conservative force such as friction depends on other factors, such as velocity and dissipative and no potential energy can be defined for them.
Hence central forces are non-conservative.
Question 3
1 / -0

A force $$(4\hat {i} + \hat {j} - 2\hat {k})N$$ acting on a body maintains its velocity at $$(2\hat {i} + 2\hat {j} + 3\hat {k})ms^{-1}$$. The power exerted is:

A
$$4\ W$$

B
$$5\ W$$

C
$$2\ W$$

D
$$8\ W$$

Solution

Force, $$\vec {F} = (4\hat {i} + \hat {j} - 2\hat {k})N$$
Velocity, $$\vec {v} = (2\hat {i} + 2\hat {j} + 3\hat {k})ms^{-1}$$
Power, $$P = \vec {F} \cdot \vec {v} = (4\hat {i} + \hat {j} - 2\hat {k})\cdot (2\hat {i} + 2\hat {j} + 3\hat {k})$$
$$= (8 + 2 - 6)W = 4\ W$$.
Question 4
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Calculate work done on object where applied force is $$10N$$ and distance is $$10m$$:

A
$$10\ J$$

B
$$50\ J$$

C
$$100\ J$$

D
$$150\ J$$

Solution

Given data
$$f=10N$$
$$d=10m$$
Work done by applied force is
$$W=Force \times distance$$
$$W = Fd $$
$$W= 10\ N\times 10\ m$$
$$W = 100\ J$$.
Question 5
1 / -0

A raindrop of mass $$1\ g$$ falling from a height of $$1\ km$$ hits the ground with a speed of $$50\ ms^{-1}$$. Which of the following statements is correct?
(Take $$g = 10\ ms^{-2})$$

A
The loss of potential energy of the drop is $$10\ J$$

B
The gain in kinetic energy of the drop is $$1.25\ J$$

C
The gain in kinetic energy of the drop is not equal to the loss of potential energy of the drop

D
All of these

Solution

$$Mass$$= $$m$$=$$1g$$ =$$\frac{1}{1000}kg$$
$$Height$$ =$$h$$ =$$1km$$ =$$1000m$$
$$Speed=50m/s$$
$$g=10m/s^2$$
The formula of potential energy, $$mgh=\cfrac{1}{1000}\times10\times1000 = 10J$$
When it hit the ground this potential energy is lost fully. The loss of potential energy of the drop is $$10J$$
Question 6
1 / -0

A block of mass $$2\ kg$$ initially at rest moves under the action of an applied horizontal force of $$6\ N$$ on a rough horizontal surface. The coefficient of friction between block and surface is $$0.1$$. The work done by the applied force in $$10\ s$$ is (Take $$g = 10\ ms^{-2})$$.

A
$$200\ J$$

B
$$-200\ J$$

C
$$600\ J$$

D
$$-600\ J$$

Solution

The various forces acting on the block is as shown in the figure.
Here, $$m = 2\ kg, \mu = 0.1, F = 6\ N, g = 10\ ms^{-2}$$

Force of friction,
$$f = \mu N = 0.1\times 2\ kg\times 10\ ms^{-2} = 2\ N$$

Net force with which the block moves
$$F' = F - f = 6N - 2N = 4N$$

Net acceleration with which the block moves
$$a = \dfrac {F'}{m} = \dfrac {4N}{2kg} = 2\ ms^{-2}$$

Distance travelled by the block in $$10\ s$$ is
$$d = \dfrac {1}{2}at^{2} = \dfrac {1}{2}\times 2\ ms^{-2}(10)^{2} = 100\ m(\therefore u = 0)$$

As the applied force and displacement are in the same direction therefore angle between the applied force and the displacement is $$\theta = 0^{\circ}$$.

Hence, work done by the applied force,
$$W_{F} = Fd\cos \theta = (6N) (100m) \cos 0^{\circ} = 600\ J$$.
Question 7
1 / -0

Mohan uses one television of $$100$$ W for $$10$$ hrs. How much energy is consumed by Mohan?

A
$$E=100 kWh$$

B
$$E=0.1 kWh$$

C
$$E=1 kWh$$

D
$$E=10 kWh$$

Solution

Energy consumption is given by $$E=P\times t$$ ,where P= power and t= time
Given power $$P=100\ W=0.1 KW$$ and time $$t=10 hour$$
$$E=1 kWh$$
Question 8
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Which of the following bodies has the largest kinetic energy?

A
Mass $$3M$$ and speed $$V$$

B
Mass $$3M$$ and speed $$2V$$

C
Mass $$2M$$ and speed $$3V$$

D
Mass $$M$$ and speed $$4V$$

Solution

We know that, the kinetic energy is

$$K.E=\dfrac{1}{2}m{{v}^{2}}....(I)$$


Checking all options given -
A) $$ m=3M $$ &  $$ v=v $$

$$ K.E=\dfrac{1}{2}m{{v}^{2}} $$

$$ K.E=\dfrac{1}{2}\times 3M\times {{v}^{2}} $$

$$ K.E=\dfrac{3M{{v}^{2}}}{2} $$

B) $$ m=3M $$ &  $$ v=2v $$

$$ K.E=\dfrac{1}{2}m{{v}^{2}} $$

$$ K.E=\dfrac{1}{2}\times 3M\times 4{{v}^{2}} $$

$$ K.E=6M{{v}^{2}} $$

C) $$ m=2M $$ & $$ v=3v $$

$$ K.E=\dfrac{1}{2}m{{v}^{2}} $$

$$ K.E=\dfrac{1}{2}\times 2M\times 9{{v}^{2}} $$

$$ K.E=9M{{v}^{2}} $$

D) $$ m=M $$ &  $$ v=4v $$

$$ K.E=\dfrac{1}{2}\times M\times 16{{v}^{2}} $$

$$ K.E=8M{{v}^{2}} $$

Hence, the largest kinetic energy is $$9M{{v}^{2}}$$ when $$m=2M$$ and $$v=3v$$.
Question 9
1 / -0

When a men walks on a horizontal surface then work done by

A
friciton is zero

B
contact force is non-zero

C
gravity is non-zero

D
None of these

Solution

When the man moves on a horizontal surface, then work done by gravity is zero since gravitational force acts perpendicular to the displacement.

And the normal force will be also perpendicular to displacement so work done by It also is zero. - - - - - - - - 1

But frictional force is acting opposite to displacement so work done by frictional force is negative. - - - - - - - - - - - 2

Using statement (1) and (2) we can say that work done by contact force is non - zero
Question 10
1 / -0

A body of mass 15 kg is raised from certain depth. If the work done in raising it by 10 m is 1620 J, its velocity at this position is

A
$$2 \ ms^{-1}$$

B
$$4 \ ms^{-1}$$

C
$$ 1\ ms^{-1}$$

D
$$8 \ ms^{-1}$$

Solution

$$ W = mgh + \dfrac{1}{2}mv^2 $$

$$ 1620 = 15 \times10 \times10 + \dfrac{1}{2} \times 15 \times v^2 $$

$$\implies v =4\ m/s $$

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Work and Energy Test - 45

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Work and Energy Test - 45

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SHARING IS CARING

Question 1

$$10W$$

$$1W$$

$$20W$$

$$2W$$

Solution

Question 2

No work is done if the displacement is perpendicular to the direction of the applied force

If the angle between the force and displacement vectors is obtuse, then the work done is negative

Frictional force is a non-conservative

All the central forces are non-conservative

Solution

Question 3

$$4\ W$$

$$5\ W$$

$$2\ W$$

$$8\ W$$

Solution

Question 4

$$10\ J$$

$$50\ J$$

$$100\ J$$

$$150\ J$$

Solution

Question 5

The loss of potential energy of the drop is $$10\ J$$

The gain in kinetic energy of the drop is $$1.25\ J$$

The gain in kinetic energy of the drop is not equal to the loss of potential energy of the drop

All of these

Solution

Question 6

$$200\ J$$

$$-200\ J$$

$$600\ J$$

$$-600\ J$$

Solution

Question 7

$$E=100 kWh$$

$$E=0.1 kWh$$

$$E=1 kWh$$

$$E=10 kWh$$

Solution

Question 8

Mass $$3M$$ and speed $$V$$

Mass $$3M$$ and speed $$2V$$

Mass $$2M$$ and speed $$3V$$

Mass $$M$$ and speed $$4V$$

Solution

Question 9

friciton is zero

contact force is non-zero

gravity is non-zero

None of these

Solution

Question 10

$$2 \ ms^{-1}$$

$$4 \ ms^{-1}$$

$$ 1\ ms^{-1}$$

$$8 \ ms^{-1}$$

Solution

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