A stationary body of mass 3 kg explodes into three equal pieces.

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61.

A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off in two mutually perpendicular directions, one with a velocity of 3 i^ ms-1 and the other with a velocity of 4 j^ ms-1. If the explosion occurs in 10-4  s, the average force acting on the third piece in newton is

  • 3i^ + 4j^ × 10-4

  • 3i^ - 4j^ × 10-4

  • 3i^ + 4j^ × 104

  • - 3i^ + 4j^ × 104


D.

- 3i^ + 4j^ × 104

By law of conservation of linear momentum

m1 v1 + m2 v2 + m3 v3 = 0

Here : m1 = m2 = m3 = 1 Kg

       v1 = 3i^,  v2 = 4j^ 3i^ + 4j^ + v3 = 0

The average force acting on the third piece is

F = m v3t   = 1 × - 3i^ + 4j^10-4 N   = - 3i^ + 4j^ × 104 N


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62.

A mass of 1 kg is just able to slide down the slope of an inclined rough surface when the angle of inclination is 60°. The minimum force necessary to pull the mass up the inclined plane (g = 10 ms-2) is

  • 14.14 N

  • 17.32 N

  • 10 N

  • 16.66 N


63.

A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass m3 is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is

  • 87 F

  • 17 F

  • 78 F

  • 15 F


64.

A bullet of mass 0.05 kg moving with a speed of 80 ms enters a wooden block and is stopped after a distance of 0.40 m. The average resistive force exerted by the block on the below is

  • 300 N

  • 20 N

  • 400 N

  • 40 N


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65.

A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below.

The velocity of the particle after 10 s is

  • 20 ms-1

  • 10 ms-1

  • 50 ms-1

  • 26 ms-1


66.

The sum of the magnitudes of two forces acting at a point is 18 N and the magnitude of their resultant is 12 N. If the resultant is at 90° with the smaller force, the magnitude of the forces in N are

  • 6, 12

  • 11, 7

  • 5, 13

  • 14, 4


67.

A mass of 6 kg is suspended by a rope of length 2 m from a ceiling. A force of 50 N in the horizontal direction is applied at the mid-point of the rope. The angle made by the rope with the vertical, in equilibrium is

  • 50°

  • 60°

  • 30°

  • 40°


68.

A shell at rest at the origin explodes into three fragments of masses 1 kg, 2 kg and m kg. The 1 kg and 2 kg pieces fly off with speeds of 5 ms-1 along x-axis and 6 ms-2 along y-axis respectively. If the m kg piece flies off with a speed of 6.5 ms-1, the total mass of the shell must be

  • 4 kg

  • 5 kg

  • 3.5 kg

  • 4.5 kg


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69.

If the road is unbanked and the coefficient of friction between the road and the tyres is 0.8, then the maximum speed with which an automobile can move around a curve of 84.5 m radius without slipping (g = 10 ms-2) is

  • 26 ms-1

  • 67.6 ms-1

  • 13 ms-1

  • 36.7 ms-1


70.

Three blocks of masses m1 m2 and m3 are connected by massless string as shown kept on a frictionless table.

     

They are pulled with a force T= 40 N. If m1 = 10 kg, m2 = 6 kg and m3 = 4 kg, the tension T2 will be

  • 20 N

  • 40 N

  • 10 N

  • 32 N


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