Two satellites $$S_1$$ and $$S_2$$ are revolving round a planet in coplanar circular orbits of radii $$r_1$$ and $$r_2$$ in the same direction, respectively. Their respective periods of revolution are $$1 \mathrm{~h}$$ and $$8 \mathrm{~h}$$. The radius of orbit of satellite $$S_1$$ is equal to $$10^4 \mathrm{~km}$$. What will be their relative speed (in $$\mathrm{km} / \mathrm{h}$$) when they are closest?
A body of mass $$4 \mathrm{~kg}$$ moving with velocity $$12 \mathrm{~m} / \mathrm{s}$$ collides with another body of mass $$6 \mathrm{~kg}$$ at rest. If two bodies stick together after collision, then the loss of kinetic energy of system is
The coefficient of cubical expansion of mercury is $$0.00018 /{ }^{\circ} \mathrm{C}$$ and that of brass $$0.00006 /{ }^{\circ} \mathrm{C}$$. If a barometer having a brass scale were to read $$74.5 \mathrm{~cm}$$ at $$30^{\circ} \mathrm{C}$$, find the true barometric height at $$0^{\circ} \mathrm{C}$$. The scale is supposed to be correct at $$15^{\circ} \mathrm{C}$$.
The particle of mass $$m$$ is moving in a circular path of constant radius $$r$$ such that its centripetal acceleration $$a_c$$ is varying with time $$t$$ as $$a_c=k^2 r t^2$$, where $$k$$ is a constant. The power delivered to particle by the forces acting on it is