A particle starts from mean position and performs S.H.M. with period 6 second. At what time its kinetic energy is $50 \%$ of total energy?
$$ \left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right) $$
Rate of flow of heat through a cylindrical rod is $\mathrm{H}_1$. The temperature of the ends of the rod are ' $\mathrm{T}_1$ ' and ' $\mathrm{T}_2$ '. If all the dimensions of the rod become double and the temperature difference remains the same, the rate of flow of heat becomes ' $\mathrm{H}_2$ '. Then $\mathrm{H}_2=$
A coil of area $12 \mathrm{~cm}^2$ has 250 turns. Magnetic field of $0.2 \mathrm{~Wb} / \mathrm{m}^2$ is perpendicular to the plane of the coil. The field is reduced to $0.1 \mathrm{~Wb} / \mathrm{m}^2$ in 0.1 second. The magnitude of induced e.m.f. in the coil is
For which of the following combinations of working temperatures, the efficiency of Carnot's engine is maximum?
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