Two bodies A and B, have thermal emissivities of 0.01 and 0.81 respectively. The outer surface areas of both the bodies are same and emit the same radiated power. The wavelength λ_B , corresponding to the maximum intensity in radiation from B, is shifted from the wavelength λ_A , corresponding to the maximum intensity in radiation from A, by 1 µm. If the temperature of A is 5802 k, then the temperature and wavelength λ_B of body B are

• 1934 K, 3.5 µm

• 1934 K, 1.5 µm

• 1728 K, 32 µm

• 1764 K, 1.8 µm

The equation of a simple harmonic wave is given by y = 3sin $\frac{\mathrm{\pi }}{2}$ (50 t - x) where, x and y are in meters and t in seconds. The ratio of maximum particle velocity to the wave velocity is 

• 2$\mathrm{\pi }$

• $\frac{3}{2}\mathrm{\pi }$

• $3\mathrm{\pi }$

• $\frac{2}{3}\mathrm{\pi }$

Two strings with mass per unit length of 9 gcm^-1 and 25 gcm^-1 are joined together in series. The reflection coefficient for the vibration waves are

• $\frac{9}{25}$

• $\frac{3}{5}$

• $\frac{1}{16}$

• $\frac{9}{16}$

An ideal heat engine exhausting heat at 27° C is to have 25% efficiency. It must take heat at

• 127 °C

• 227° C

•  327° C

• None of these

A magnet is made to oscillate with a particular frequency, passing through a coil as shown in the figure. The time variation of the magnitude of emf generated across the coil during one cycle is

Two spherical soap bubbles of radii r₁ and r₂ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to

• $\frac{{\mathrm{r}}_1 + {\mathrm{r}}_2}{2}$

• $\frac{{\mathrm{r}}_1{\mathrm{r}}_2}{{\mathrm{r}}_1 + {\mathrm{r}}_2}$

• $\sqrt{{\mathrm{r}}_1{\mathrm{r}}_2}$

• $\sqrt{{{\mathrm{r}}_1}^2 + {{\mathrm{r}}_2}^2 }$

27.

A wooden block is floating on water kept in a beaker, 40% of the block is above the water surface. Now the beaker is kept inside a lift that starts going upward with acceleration equal to $\frac{\mathrm{g}}{2}$. The block will then

• sink

• float with 10% above the water surface

• float with 40% above the water surface

• float with 70% above the water surface

A bar magnet has a coercivity of 4 x 10³ Am^-1. It is placed inside a solenoid of length 12 cm having 60 turns in order to demagnetise it. The amount of current that should be passed through the solenoid is

• 16 A

• 8 A

• 4 A

• 2 A

A series R-L-C circuit driven with E_rms = 100V and frequency f_d = 50 Hz is shown below.

What new capacitance should be connected to maximize the average power, if other parameters of the circuit are not changed ?

• 41.6 µF

• 33.5 µF

• 39.8 µF

• 31.3 µF

A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be

• $\frac{\mathrm{M}}{2}$

• M

• $\frac{3\mathrm{M}}{\mathrm{\pi }}$

• $\frac{2\mathrm{M}}{\mathrm{\pi }}$