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 $3 \hat{\mathrm{i}}$ ms^-1 and the other with a velocity of $4 \hat{\mathrm{j}}$ ms^-1. If the explosion occurs in 10^-4  s, the average force acting on the third piece in newton is

• $\left(3\hat{\mathrm{i}} + 4\hat{\mathrm{j}}\right) \times {10}^{-4}$

• $\left(3\hat{\mathrm{i}} - 4\hat{\mathrm{j}}\right) \times {10}^{-4}$

• $\left(3\hat{\mathrm{i}} + 4\hat{\mathrm{j}}\right) \times {10}^4$

• $- \left(3\hat{\mathrm{i}} + 4\hat{\mathrm{j}}\right) \times {10}^4$

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

A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass $\left(\frac{\mathrm{m}}{3}\right)$ 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

• $\frac{8}{7} \mathrm{F}$

• $\frac{1}{7} \mathrm{F}$

• $\frac{7}{8} \mathrm{F}$

• $\frac{1}{5} \mathrm{F}$

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

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

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

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

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

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 T₃ = 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