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

12.

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

A rod AB of mass 10 kg and length 4 m rests on a horizontal floor with end A fixed so as to rotate it in vertical plane about perpendicular axis passing through A. If the work done on the rod is 100 J, the height to which the end B be raised vertically above the floor is

• 1.5 m

• 2.0 m

• 1.0 m

• 2.5 m

A particle is released from a height S. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

• $\frac{\mathrm{S}}{4}, \frac{3\mathrm{gS}}{2}$

• $\frac{\mathrm{S}}{4}, \frac{\sqrt{3\mathrm{gS}}}{2}$

• $\frac{\mathrm{S}}{2}, \frac{3\mathrm{gS}}{2}$

• $\frac{\mathrm{S}}{4}, \sqrt{\frac{3\mathrm{gS}}{2}}$

An electric pump is used to fill an overhead tank of capacity 9 m³ kept at a height of 10 m above the ground. If the pump takes 5 min to fill the tank by consuming 10 kW power, the efficiency of the pump should be (Take g = 10 ms^-2)

• 60 %

• 40 %

• 20 %

• 30 %

A sphere of mass m and redius r rolls on a horizontal plane without slipping with the speed u. Now, if it rolls up vertically, the maximum height it would attain will be

• $\frac{3{\mathrm{u}}^2}{4\mathrm{g}}$

• $\frac{5{\mathrm{u}}^2}{2\mathrm{g}}$

• $\frac{7{\mathrm{u}}^2}{10\mathrm{g}}$

• $\frac{{\mathrm{u}}^2}{2\mathrm{g}}$

If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be

• 3 h

• 1.5 h

• 6 h

• 4 h

A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01 R. The period of second satellite is longer than the first one (approximately) by

• 1.5 %

• 0.5 %

• 3 %

• 1 %

The change in potential energy when a body of mass m is raised to a height nR from earth's surface is (R = radius of the earth)

• $\mathrm{mgR} \frac{\mathrm{n}}{\left(\mathrm{n} - 1\right)}$

• mgR

• $\mathrm{mgR} \frac{\mathrm{n}}{\left(\mathrm{n} + 1\right)}$

• $\mathrm{mgR} \frac{{\mathrm{n}}^2}{\left({\mathrm{n}}^{2 }+ 1\right)}$

The escape velocity of body on the surface of earth is 11.2 km/s. If the mass of the earth is doubled and its radius halved, the escape velocity becomes

• 5.6 km/s

• 11.2 km/s

• 22.4 km/s

• 44.8 km/s