Work Energy and Power Test

Result

Work Energy and Power Test - 76

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$-10J$$

B
$$100J$$

C
$$10J$$

D
$$1J$$

Solution
Question 2
1 / -0

A bullet of mass $$m$$ and speed $$v$$ hits a pendulum bob of mass $$M$$ at time $$t _ { 1 }$$ and passes completely through the bob. The bullet emerges at time $$t _ { 2 }$$ with a speed of $$v / 2$$. The pendulum bob is suspended by a stiff rod of length $$l$$ and negligible mass. After the collision, the bob can barely swing through a complete vertical circle.At time $$t _ { 3 }$$ , the bob reaches the highest position.What quantities are conserved in this process?

A
Total kinetic energy of the bob and the bullet during the time interval $$\Delta t = t _ { 2 } - t _ { 1 }$$

B
Total momentum of the bob and the bullet during the time interval $$\Delta t = t _ { 2 } - t _ { 1 } $$

C
Total mechanical energy of the bob and the bullet during the time interval $$t _ { 3 } - t _ { 1 } $$

D
Momentum of the bob after $$t _ { 2 }$$

Solution
Question 3
1 / -0

A ball of mass m is moving with a speed $$20\ m/sec$$. It strikes an identical ball which is at rest. After collusion each ball moves making an angle of $${ 45 }^{ \circ }$$ with the original of motion. Calculate their speeds after collision.

A
$$10\sqrt { 3} m/sec\quad$$ for each ball

B
$$20\sqrt { 2} m/sec\quad $$ for each ball

C
$$30\sqrt { 2 } m/sec\quad $$ for each ball

D
$$10\sqrt { 2 } m/sec\quad $$ for each ball

Solution
Question 4
1 / -0

A particle is displaced from (1, 2) m to (0,0) m along the path $$y = 2x^3$$. Work done by a force $$\vec F = (x^3 \hat j + y \hat i)$$ N acting on the particle, during this displacement, is

A
-1.5 J

B
1.5 J

C
2.5 J

D
-2.5 J

Solution
Question 5
1 / -0

A particle of mass m moves on a straight line with its velocity varying with the distance travelled according to the equation $$v = a\sqrt{x}$$, where a is constant. Find the total work done by all the forces during a displacement from x = 0, to x = d.

A
$$ 5 ma^2 \ d/2$$

B
$$ ma^3 \ d/2$$

C
ma d/2

D
$$ ma^2 \ d/2$$

Solution
Question 6
1 / -0

A force $$\overrightarrow { F } =\left( 3t\hat { i } +5\hat { j } \right) N$$ acts on a body and its displacement varies as $$\overrightarrow { S } =\left( 2{ t }^{ 2 }\hat { i } -5\hat { j } \right). $$ work done by this force in $$t=0$$ to $$2sec$$ is

A
$$23 J$$

B
$$32 J$$

C
$$Zero$$

D
$$can't$$ $$obtained$$

Solution
Question 7
1 / -0

A skater of weight $$30 \ kg$$ has initial speed $$32m/s$$ and second one of weight $$40 \ kg$$ has $$5m/s$$. After the collision, they stick together and have a speed $$5m/s$$. Then the loss in KE is

A
$$48J$$

B
$$96J$$

C
Zero

D
None of these

Solution

Given:
Weight of the skater 1 is $$m_1=30 \ kg$$
His initial speed $$u_1=32 \ m/s$$
Weight of the skater 2 is $$m_2=40 \ kg$$
His initial speed $$u_2=5 \ m/s$$
After collision they stick together
Both of their speed $$v_1=v_2=v=5 \ m/s$$

We know that kinetic energy $$=\dfrac{1}{2}mv^2$$
Initial kinetic energy $$=KE_{skater 1}+KE_{skater 2}$$
$$=\dfrac{1}{2}m_1u_1^2+\dfrac{1}{2}m_2u_2^2$$
$$=\dfrac{1}{2}(30)(32)^2+\dfrac{1}{2}(40)(5)^2$$
$$=\dfrac{1}{2}(30)(1024)+\dfrac{1}{2}(40)(25)$$
$$=15360+500=15860 \ J$$
Final kinetic energy $$=\dfrac{1}{2}m_1v_1^2+\dfrac{1}{2}m_2v_2^2$$
$$=\dfrac{1}{2}m_1v^2+\dfrac{1}{2}m_2v^2=\dfrac{1}{2}(m_1+m_2)v^2$$
$$=\dfrac{1}{2}(30+40)(5)^2$$
$$=\dfrac{1}{2}(70)(25)=875 \ J$$

Loss in kinetic energy $$\Delta KE=15860-875$$
$$=14985 \ J$$
The answer is none of the given options. So option D is the answer.
Question 8
1 / -0

A massive disc of radius $$R$$ is moving with a constant velocity $$u$$ on an frictionless table. Another small disc collides with it elastically with a speed of $$v_{0} = 0.3\ m/s$$, the velocities of the discs are parallel. The distance $$d$$ shown in the figure is equal to $$R/2$$, friction between the discs is negligible.
For which $$u$$ (in m/s) will the small disc move perpendicular to its original motion after the collision?

A
$$1$$

B
$$0.1$$

C
$$2$$

D
$$0.2$$
Question 9
1 / -0

A ball is dropped from a height of 10m. It strikes the ground and rebounds up to a height of 2.5m. During the collision the percent loss in kinetic energy is?

A
25%

B
50%

C
75%

D
100%

Solution
Question 10
1 / -0

A particle of mass m moves along the quarter section of the circular path whose centre is at the origin. the radius of the circular path is a.. A force $$ \overrightarrow F = y \hat i - x\hat j $$ newton acts on the particle, where x. y denote the coordinates of position of the particle. calculate the work done by this force in taking the particle from point A (a, 0) to point B(0, a) along the circular path.

A
$$ \frac { \pi a^2}{4} J $$

B
$$ \frac { \pi a^2}{2} J $$

C
$$ -\frac { \pi a^2}{2} J $$

D
$$ -\frac { \pi a^2}{4} J $$

Solution