The potential energy of a particle of mass 1 kg free to move along the X-axis is given by \(U(x) = (3x^2-4x+6)~\text{J}\). The force acting on the particle at x = 0 will be:

1.  2i^ N

2.  -4i^ N

3.  5i^ N

4.  4i^ N

Subtopic:  Potential Energy: Relation with Force |
 61%
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A block of mass m is attached with a spring of spring constant k as shown in the figure. Another block of mass 2m moving with speed v hits the spring. Speed of blocks at the instant of maximum compression of spring is:

                            

1.  v3

2.  v2

3.  2v3

4.  3v2

Subtopic:  Collisions |
 76%
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The potential energy of a particle of mass m varies as U=ax2+by. The magnitude of the acceleration of the particle at (0, 3) is (symbols have their usual meaning)

1.  bm

2.  3bm

3.  bm

4.  Zero

Subtopic:  Potential Energy: Relation with Force |
 64%
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A ball of mass 100 g at rest is thrown on a horizontal surface as shown in the figure. The acceleration-displacement graph for the motion is given. The maximum height attained by the ball on the smooth inclined plane is

               

(1)  10 m

(2)  4 m

(3)  2 m

(4)  1 m

Subtopic:  Work Energy Theorem |
 73%
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A body moving with speed 10 m/s is stopped by applying constant braking power in 5 seconds. If the speed of the body is 30 m/s, then time in which the body can be stopped by applying the same retarding power is

(1)  10 s

(2)  15 s

(3)  30 s

(4)  45 s

Subtopic:  Power |
 50%
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A 50 kg straight uniform rod of length 2 m is lying on a horizontal floor. If a man successfully tries to erect the rod at 60° with vertical, then the amount of work done by the man is

(1)  250 J

(2)  200 J

(3)  150 J

(4)  500 J

Subtopic:  Gravitational Potential Energy |
 51%
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A small ball is given a velocity 2gl on the smooth horizontal floor which leads to a smooth vertical circular path. The ball will Smooth

                     

(1)  complete the loop.

(2)  reach only up to point P.

(3)  reach to point Q.

(4)  leave the contact somewhere between P and Q.

Subtopic:  Work Energy Theorem |
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A vertically compressed spring of constant k releases a ball of mass m as shown in the figure. The maximum height attained by the ball from the compressed point is (x is the initial compression in the spring)

                                

1.  kx22mg

2.  kx2mg

3.  kx24mg

4.  2kx2mg

Subtopic:  Elastic Potential Energy |
 82%
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Work done the spring force in a time interval maybe

(1)  Positive

(2)  Negative

(3)  Zero

(4)  All of these

Subtopic:  Elastic Potential Energy |
 77%
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A body of mass m moving with velocity v in X-direction collides with another identical body moving with the same speed in the y-direction. They coalesce into one body during a collision. The direction of motion of the composite body after the collision is

(1)  30' with X-axis

(2)  45° with X-axis

(3)  60° with X-axis

(4)  Along the y-axis

Subtopic:  Collisions |
 87%
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