The relationship between force and position is shown in the figure given (in one dimensional case). Find the work done by the force in displaying a body from x= 1 cm to x= 5cm is   [This question is only for Dropper and XII batch]

1. 10 erg

2. 20 erg

3. 30 erg

4. 40 erg

Concept Questions :-

Integration
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The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure. The mass of the body is 25 kg and initial velocity is 2 m/s. When the distance covered by the body is 4 m, its kinetic energy would be    [This question is only for Dropper and XII batch]

1. 50 J

2. 40 J

3. 20 J

4. 10 J

Concept Questions :-

Integration
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A long spring is stretched by 2 cm, its potential energy is U. If the spring is streched by 10 cm, find the potential energy stored in it.   [This question is only for Dropper and XII batch]

1. 10 U

2. 15 U

3. 20 U

4. 25 U

Concept Questions :-

Integration
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A spring of spring constant  is stretched initially by 5 cm from the unstretched position. Find the work required to stretch it further by another 5 cm is   [This question is only for Dropper and XII batch]

1. 15 J

2. 18.75 N .m

3. 20 J

4. 22.75 N .m

Concept Questions :-

Integration
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A constant force F is applied on a body. The power (P) generated is related to the time elapsed (t) as

[This question is only for Dropper and XII batch]

1.

2.

3.

4.

Concept Questions :-

Integration
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The gravitational field due to a mass distribution is given by , where k is a constant. Assuming the potential to be zero at infinity, find the potential at a point x = a. [This question is only for Dropper and XII batch]

1. $\frac{k}{{a}^{2}}$

2. $\frac{-k}{{a}^{2}}$

3. $\frac{k}{a}$

4. $\frac{-k}{a}$

Concept Questions :-

Integration
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Electric field is given by E $=\frac{100}{{x}^{2}}$ . Find the potential difference between x= 10 and x= 20 m. [This question is only for Dropper and XII batch]

1. 5 V

2. 10 V

3. 15 V

4. 20 V

Concept Questions :-

Integration
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Calculate the electric field on the axis of a very long uniformly charged, thin rod at a distance r from one end. The charge per unit length of the rod is $\lambda$[This question is only for Dropper and XII batch]

1. $\frac{2k\lambda }{r}$

2. $\frac{k\lambda }{r}$

3. $\frac{k\lambda }{2r}$

4. $\frac{k\lambda }{4r}$

Concept Questions :-

Integration
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Find electric field due to a uniformly charged, long and thin rod

[This question is only for Dropper and XII batch]

1. $\frac{k\lambda }{r}$

2. $\frac{k\lambda }{2r}$

3. $\frac{2k\lambda }{r}$

4. $\frac{k\lambda }{4r}$

Concept Questions :-

Integration
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A 10 kg mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x=0 to x=8 cm [This question is only for Dropper and XII batch]

1.

2.

3.

4.

Concept Questions :-

Integration
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Difficulty Level: