Look at the graphs (a) to (d) carefully and indicate which of these possibly represents one dimensional motion of a particle ?

A cyclist starts from the centre O of a circular park ofradius 1 km, reaches the edge P of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes 10 mm, the net displacement and average speed of the cyclist (in metre and kilometre per hour) are

• 0, 1

• $\frac{\mathrm{\pi } + 4}{2}, 0$

• $21.4, \frac{\mathrm{\pi } + 4}{2}$

• 0, 21.4

When a low flying aircraft passes over head, we sometimes notice a slight shaking of the picture on our TV screen. This is due to 

• diffraction of the signal received from the antenna

• interference of the direct signal received by the antenna with the weak signal reflected by the passing aircraft

• change ofmagenetic flux occuring due to the passage of aircraft

• vibration created by the passage of aircraft

The physical quantity having the dimensions [M^-1L^-3T³A²] is

• resistance

• resistivity

• electrical conductivity

• electromotive force

A satellite in a circular orbit of radius R has a period of 4 h. Another satellite with orbital radius 3 R around the same planet will have a period (in hours)

• 16

• 4

• $4\sqrt{27}$

• $4\sqrt{8}$

The unit of Stefan's constant is

• Wm^-2K^-1

• WmK^-4

• Wm^-2K^-4

• Nm^-2K^-4

For ordinary terrestrial experiments, the observer in an inertial frame in the following cases is

• a child revolving in a giant wheel

• a driver in a sports car moving with a constant high speed of 200 kmh^-1 on a straight rod

• the pilot of an aeroplane which is taking off

• a cyclist negotiating a sharp curve

If white light is used in the Newton's rings experiment, the colour observed in the reflected light is complementary to that observed in the transmitted light through the same point. This is due to

• 90° change of phase in one of the reflected waves

• 180° change of phase in one of the reflected waves

• 145° change of phase in one of the reflected waves

• 45° change of phase in one of the reflected waves

 A simple pendulum has a length l and the mass of the bob is m. The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\sqrt{\mathrm{g} + {\displaystyle \frac{\mathrm{qE}}{\mathrm{m}}}}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\sqrt{\mathrm{g} - {\displaystyle \frac{\mathrm{qE}}{\mathrm{m}}}}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\sqrt{{\mathrm{g}}^2 + {\left({\displaystyle \frac{\mathrm{qE}}{\mathrm{m}}}\right)}^2}}}$

The freezer in a refrigerator is located at the top section so that

• the entire chamber of the refrigerator is cooled quickly due to convection

• the motor is not heated

• the heat gained from the environment is high

• the heat gained from the environment is low