Physics

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate dm(t)/dt$$ =bv^2(t), where v(t)$$ its instantaneous velocity. The instantaneous acceleration of the satellite is:

A parallel plate capacitor has plate of length ' $$ l', width ' w$$ ' and separation of plates is 'd $$ '. It is connected to a battery of emf V$$ . A dielectric slap of the same thickness 'd $$ ' and of dielectric constant $$ k = 4 is being, inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored?

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 400 Hz$\frac{}{{}_{}}\frac{}{{}_{}{}^{}}$ to 400 Hz$\frac{}{{}_{}{}^{}}$ , when it gets reflected from the wall. If the speed of sound in air is 345 m/s$$ , then the speed of the car is:

Ten charges are placed on the circumference of a circle of radius $10\mathrm{s}$ $$ with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q)$$ each, while $\mathrm{2,4},\mathrm{6,8},10$ $$ have charge $$ (-q)each. The potential v$$ and the electric field $$ E at the centre of the circle are respectively: (Take V = 0 $$ at infinity)

The correct match between the entries in column I and column II are:

An iron rod of volume ${10}^{-3}{\mathrm{m}}^3$ ${}^{}{}^{}$ and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of $0.5\mathrm{A}$ $$ is passed through the solenoid, then the magnetic moment of the rod will be:

In adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be $n$ $$ times the initial pressure. The value of $n$ $$ is:

In the circuit shown, charge on the $5\mu \mathrm{F}$ $$ capacitor is:

Two different wires having lengths $L_1$ ${}_{}$ and ${}_{}$ $L_2$ , and respective temperature coefficient of linear 4expansion ${\alpha }_1$ ${}_{}$ and ${\alpha }_2$ ${}_{}$ , are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

Two coherent sources of sound, $S_1$ ${}_{}$ and $S_2$ ${}_{}$ produce source waves of the same wavelength, $\lambda =1\mathrm{m}$ $$ , in phase. $S_1$ ${}_{}$ and ${\mathrm{S}}_2$ ${}_{}$ are placed $1.5\mathrm{m}$ $$ apart (see fig). A listener located at $\mathrm{L}$ $$ , directly in front of $S_2$ ${}_{}$ finds that the intensity is at a minimum when he is $2\mathrm{m}$ $$ away from ${\mathrm{S}}_2$ ${}_{}$ . The listener moves away from $S_1$ ${}_{}$ , keeping his distance from $S_2$ ${}_{}$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ $$ from ${}_{}$ $S_1$ . Then, $d$ $$ is: