Work Energy and Power Test

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Work Energy and Power Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

A $$110 kg$$ panda is riding on a $$3.0 m$$ long swing whose mass can be considered negligible. The highest point of its arc occurs when the swing makes a $${20}^{o}$$ angle with the vertical.
What is the magnitude of the total tension in the ropes of the swing at that point?

A
$$0N$$

B
$$103 N$$

C
$$369 N$$

D
$$1013 N$$

E
$$1078 N$$

Solution

Given : $$m =110$$ kg
Tension in the string $$T = mg$$ $$cos20^o = 110 \times 9.8 \times 0.94 = 1013$$ N
Question 2
1 / -0

The correct formula to find the velocity of a body with kinetic energy '$$k$$' is:

A
$$V=\dfrac{2k}{m}$$

B
$$V=\sqrt{\dfrac{2k}{m}}$$

C
$$V=\dfrac{4{k}^{2}}{m}$$

D
$$V=\dfrac{1}{2}km$$

Solution

Kinetic energy of a body is given by
$$k=\dfrac{1}{2}mv^2$$

$$v^2$$ = $$\dfrac{2k}{m}$$

$$v=\sqrt {\dfrac{2k}{m}}$$.

Hence, answer is option B.
Question 3
1 / -0

The position function of a particle is given by $$x\left(t\right)=k{t}^{{5}/{2}}$$, where $$k$$ is a constant.
If the particle starts at rest and is propelled through some distance $$d$$ so that the trajectory matches $$x\left(t\right)$$, the work done on the particle is proportional to which power of $$t$$?

A
$${t}^{5}$$

B
$${t}^{3}$$

C
$${t}^{{5}/{2}}$$

D
$${t}^{{3}/{2}}$$

E
Not enough information

Solution

$$x=kt^{5/2}$$
Speed of the particle is $$v=\dfrac{dx}{dt}=\dfrac{5}{2}kt^{3/2}$$

The acceleration of the particle becomes $$a=\dfrac{dv}{dt}=\dfrac{15}{4}kt^{1/2}$$

Force acting on particle is given by $$ma=\dfrac{15}{4}mkt^{1/2}$$

Hence the work done is given by $$F.x\propto t^{3}$$
Question 4
1 / -0

A body is acted upon by a force which is proportional to the distance covered. If distance covered by denoted by x, then work done by the force will be proportional to:

A
$$x$$

B
$$x^2$$

C
$$x^{\dfrac{3}{2}}$$

D
$$x^4$$

Solution

Here, Force $$F\propto x$$ or $$F=cx$$ where c is propotionality constant
Work done $$W=Fx=cx\times x=cx^2$$
So, $$W\propto x^2$$
Question 5
1 / -0

A small stone tied to an inextensible string of negligible mass is rotated in a circle of radius $$2 m$$ in a vertical plane. Find the speed at a horizontal point on the circle. (in $$m/s$$)

A
$$7.67$$

B
$$2.36$$

C
$$6.32$$

D
$$8.32$$

Solution

$$ v= \sqrt {3gr}$$
$$ v= \sqrt {3 * 9.8* 2} = 7.67 m/s $$
Question 6
1 / -0

A stone of mass $$10 kg$$ tied with a string of length $$0.5 m$$ is rotated in a vertical circle. Find the total energy of the stone at the highest position. (in $$J$$)

A
$$123.36$$

B
$$122.5$$

C
$$154.3$$

D
$$185.6$$

Solution

assume that potential energy at lowest point is zero and stone is rotating with critical velocity
so the magnitude of velocity at highest point is $$v=\sqrt { gl } $$ where $$l=$$length of string
total energy $$E=K.E.+P.E.$$
$$\Rightarrow K.E.=\dfrac { 1 }{ 2 } m{ v }^{ 2 }=\dfrac { 1 }{ 2 } 10\times { (\sqrt { 9.8\times 0.5 } ) }^{ 2 }=24.5J$$
$$P.E.=mgh=mg(2l)=10\times 9.8\times \left( 2\times 0.5 \right) =98J$$
so the total energy $$E=98+24.5=122.5J$$
Question 7
1 / -0

Under the action of a force $$F=Cx$$, the position of a body changes from $$0$$ to $$x$$. The work done is :

A
$$\cfrac { 1 }{ 2 } C{ x }^{ 2 }$$

B
$$C{ x }^{ 2 }$$

C
$$Cx$$

D
$$\cfrac { 1 }{ 2 } C{ x }$$

Solution

Work done $$W = \int^x_0 Fdx$$
$$W = \int^x_0 Cxdx$$
$$W = C\times \dfrac{x^2}{2}\bigg|^x_0$$
$$\therefore$$ $$W = \dfrac{C}{2}\times (x^2-0 )$$ $$\implies W = \dfrac{1}{2}Cx^2$$
Question 8
1 / -0

A $$2kg$$ object is moving at $$3m/s$$. A $$4N$$ force is applied in the direction of motion and then removed after the object has travelled an additional $$5m$$. The work done by this force is:

A
$$10 J$$

B
$$15 J$$

C
$$20 J$$

D
$$25 J$$

Solution

intial velocity $$u=3m/s$$
final velocity $$v^2=u^2+2as=3^2+(2 \times 2 \times 5)=29$$ $$\implies v=5.3m/s$$

$$KE=\dfrac{1}{2}m(v^2-u^2)=\dfrac{1}{2} \times 2 \times {((5.3)^2-3^2)}=20J$$
Question 9
1 / -0

Calculate the work done in moving a cart from $$x=a$$ to $$x=b$$ whose mass is $$3kg$$ and the given surface is frictionless. $$(Take\ g=9.8m/s^{2})$$

A
$$0$$

B
$$3g(a-b)$$

C
$$3g$$

D
$$3g(a+b)$$

Solution

Since the cart is at the same level at final and initial position with respect to reference line. The net change in potential energy is zero. Also, the kinetic energy of a cart at rest is zero.
Question 10
1 / -0

A $$200 g$$ mass is whirled in a vertical circle making $$60$$ revolutions per minute. What is the tension in the string at the top of the circle if the radius of the circle is $$0.8 m$$? (in $$N$$)

A
$$6.3$$

B
$$2.36$$

C
$$4.35$$

D
$$4.23$$

Solution

$$ w = 60 \space \text {revolutions per minute }= 60 * 2\pi / 60 \space\space\text {rad/ sec} = 2\pi \space\space rad/ sec $$
$$ 200 gm = 0.2 kg $$
$$ T = mrw^2 - mg $$
$$ T = 0.2* 0.8 * (2\pi)^2 - 0.2* 9.8 $$
$$ T = 4.35 N$$

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Re-Attempt Weekly Quiz Competition

Work Energy and Power Test - 37

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Work Energy and Power Test - 37

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SHARING IS CARING

Question 1

$$0N$$

$$103 N$$

$$369 N$$

$$1013 N$$

$$1078 N$$

Solution

Question 2

$$V=\dfrac{2k}{m}$$

$$V=\sqrt{\dfrac{2k}{m}}$$

$$V=\dfrac{4{k}^{2}}{m}$$

$$V=\dfrac{1}{2}km$$

Solution

Question 3

$${t}^{5}$$

$${t}^{3}$$

$${t}^{{5}/{2}}$$

$${t}^{{3}/{2}}$$

Not enough information

Solution

Question 4

$$x$$

$$x^2$$

$$x^{\dfrac{3}{2}}$$

$$x^4$$

Solution

Question 5

$$7.67$$

$$2.36$$

$$6.32$$

$$8.32$$

Solution

Question 6

$$123.36$$

$$122.5$$

$$154.3$$

$$185.6$$

Solution

Question 7

$$\cfrac { 1 }{ 2 } C{ x }^{ 2 }$$

$$C{ x }^{ 2 }$$

$$Cx$$

$$\cfrac { 1 }{ 2 } C{ x }$$

Solution

Question 8

$$10 J$$

$$15 J$$

$$20 J$$

$$25 J$$

Solution

Question 9

$$0$$

$$3g(a-b)$$

$$3g$$

$$3g(a+b)$$

Solution

Question 10

$$6.3$$

$$2.36$$

$$4.35$$

$$4.23$$

Solution

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