Work Energy and Power Test

Result

Work Energy and Power Test - 69

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Weekly Quiz Competition

Question 1
1 / -0

The graph below represents the relation between displacement $$x$$ and force $$F$$. The work done in displacing an object from $$x=8\ m$$ to $$x=16\ m$$ is approximately.

A
$$25\ J$$

B
$$40\ J$$

C
$$8\ J$$

D
$$16\ J$$
Question 2
1 / -0

What is the amount of work done in raising a glass of water weighing $$0.5 kg $$ through a height of $$50 cm ? (g = 10 m/s ^2 $$ )

A
$$1 J $$

B
$$ 0.4 J $$

C
$$ 0.20 J $$

D
$$ 2.5 J $$

Solution

The amount of the work done in raising the glass of the water through a height is calculated by the amount of potential energy

$$W = mgh$$

By substituting the value in the above equation we get

$$W = 0.5 \times 10 \times 0.5$$

Hence the work done in raising the glass is$${\rm{2}}{\rm{.5J}}$$
Question 3
1 / -0

A mass $$m$$ is revolving in a vertical circle at the end of a string of length $$20\ cm$$. By how much times does the tension of the string at the lowest point exceed the tension at the topmost point-

A
$$2\ mg$$

B
$$4\ mg$$

C
$$6\ mg$$

D
$$8\ mg$$

Solution

Let tension $$T_1$$ at top most point is given by
$$T_1 + mg = \dfrac{mV^2_1}{l}$$ ...(1)

similarly, the tension $$T_2$$ at the lowest point is given by
$$T_2 -mg = \dfrac{mV_2^2}{l}$$ ...(1)

here, tension acting in words while balancing centrifugal force and weight of the body acting outwards
$$T_2 - T_1 = \dfrac{mv^2_2}{l} +mg - \dfrac{mv_1^2}{l} +mg$$

$$\dfrac{m}{l} (v^2_2 -V^2_1) + 2mg$$

we know from kilometres
$$v^2_1 = v^2_2 - 2g(2l)$$
$$T_2 T_1 = \dfrac{m}{l} [2g(2l)] +2mg$$

$$= 6mg$$
Hence (C) is correct answer
Question 4
1 / -0

Two steel spheres approach each other head on with the same speed and collide elastically. After the collision one of the sphere's of radius r comes to rest, the radius of the other sphere is

A
$$\frac{r}{{{{\left( 3 \right)}^{\frac{1}{3}}}}}$$

B
$$\frac{r}{3}$$

C
$$\frac{r}{9}$$

D
$${\left( 3 \right)^{\frac{1}{2}}}r$$

Solution
Question 5
1 / -0

An object of mass $$M_1$$ moving horizontally with speed u collides elastically with another object of mass $$M_2$$ at rest. Select correct statement.

A
The momentum of system is conserved only in direction PQ.

B
Momentum of $$M_1$$ is conserved in direction perpendicular to SR.

C
Momentum of $$M_2$$ is conserved in direction perpendicular to CR.

D
All of these

Solution
Question 6
1 / -0

As shown in the given figure the ball is given sufficient velocity at the lowest point to complete the circle. Length of string is $$1m$$. Find the tension in the string, when it is at $$60^{\circ}$$ with vertical position.
(Mass of ball $$= 5\ kg$$).

A
$$160\ N$$

B
$$180\ N$$

C
$$200\ N$$

D
$$225\ N$$

Solution
Question 7
1 / -0

A ball of radius r moving with a speed v collides elastically with another identical stationary ball. The impact parameter for the collision is b as shown in figure.

A
The balls must scatter at right angles for $$0 < b \le 2r.$$

B
For a head on collision b must be zero, and for an oblique collision $$0

C
After collisions, ball-1 will comes to rest and ball-2 move at an angle $$\sin^{-1} (b/r)$$ below the x-axis

D
After collision ball-1 and 2 will move at angles $$cos^{-1} (b/r) $$and $$\sin^{-1} (b/2r) above and below the x-axis respectively.

Solution
Question 8
1 / -0

A stone of mass $$1kg$$ is tied to one end of a string of length $$0.5\ m$$. It is whirled in a veretical circular. If the maximum tension in the string is $$58.8N$$, the velocity at the top is

A
$$1.82\ ms^{-1}$$

B
$$2.2\ ms^{-1}$$

C
$$3.26\ ms^{-1}$$

D
$$2.87\ ms^{-1}$$

Solution
Question 9
1 / -0

If increase in linear momentum of a body is 50%, then change in its kinetic energy is

A
25%

B
125%

C
150%

D
50%

Solution
Question 10
1 / -0

In the figure shown initially spring is in uninstructed state & blocks are at rest. Now $$100N$$ force is appiled on block $$A$$ and $$B$$ as shown in figure. After some time velocity of $$'A'$$ becomes $$2m/s$$ and that of $$'B'\ 4m/s$$ and block $$A$$ displaced by amount $$10\ cm$$ and spring is streched by amount $$30\ cm$$. then find the work done by sprig force on $$A$$.

A
$$9/3\ J$$

B
$$-6\ J$$

C
$$6\ J$$

D
$$-2 J$$