A force acts on a 3.0 g particle in such a way that the position of the particle as a function of time is given by x = 3 t – 4 t^{ 2} + t^{ 3,} where x is in meter and t in second. The work done during the first 4 s is

(A)

570 mJ

(B)

450 mJ

(C)

490 mJ

(D)

528 mJ

Question-2

The identical balls A and B moving with velocities + 0.5 m/s and -0.3 m/s respectively collide head on elastically. The velocity of the balls A and B after collision will be respectively

(A)

+ 0.5 m/s and +0.3 m/s

(B)

-0.3 m/s and +0.5 m/s

(C)

+0.3 m/s and 0.5 m/s

(D)

-0.5 m/s and +0.3 m/s

Question-3

If the momentum of a body is increased by 150% then the percentage increase in its kinetic energy is

(A)

50%

(B)

100%

(C)

125%

(D)

200%

Question-4

A child swinging a swing. Minimum and maximum heights of swing from earth’s surface are 0.75 m and 2m respectively. The maximum velocity of this swing is

(A)

5 m/s

(B)

10 m/s

(C)

15 m/s

(D)

20 m/s

Question-5

The KE acquired by a mass m in traveling a certain distance d, starting from rest, under the action of a constant force is directly proportional to

(A)

m

(B)

(C)

(D)

independent of m

Question-6

A body of mass m moving with velocity 3 km/h collides with a body of mass 2.m at rest. Now the coalesced mass starts to move with a velocity

(A)

1 km/h

(B)

2 km/h

(C)

3 km/h

(D)

4 km/h

Question-7

A position dependent force F=(7–2x + 3x^{2}) N acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5m.

Work done in joule is

(A)

35

(B)

70

(C)

135

(D)

270

Question-8

Water falls from a height of 60 m at the rate of 15kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine? (Take g = 10 m/s^{2})

(A)

8.1 kW

(B)

10.2 kW

(C)

12.3 kW

(D)

7.0 kW

Question-9

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from east with the spring initially unstretched. The maximum extension produced in the length of the spring will be

(A)

mg/k

(B)

2mg/k

(C)

4mg/k

(D)

mg/2k

Question-10

A particle of mass m_{1} is moving with a velocity v_{1} and another particle of mass m_{2} is moving with a velocity v_{2}. Both of them have the same momentum but their different kinetic energies are E_{1} and E_{2} respectively. If m_{1}> m_{2}, then

(A)

E_{1} < E_{2 }

(B)

(C)

E_{1} > E_{2 }

(D)

E_{1} = E_{2}

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