The radius of earth is $$6400 \mathrm{~km}$$ and acceleration due to gravity $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$. For the weight of body of mass $$5 \mathrm{~kg}$$ to be zero on equator, rotational velocity of the earth must be (in $$\mathrm{rad} / \mathrm{s}$$ )

A car sounding a horn of frequency $$1000 \mathrm{~Hz}$$ passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is $$11: 9$$. If the speed of sound is '$$v$$', the speed of the car is

The time period of a simple pendulum inside a stationary lift is '$$T$$'. When the lift starts accelerating upwards with an acceleration $$\left(\frac{\mathrm{g}}{3}\right)$$, the time period of the pendulum will be

The mutual inductance of a pair of coils, each of '$$N$$' turns, is '$$M$$' henry. If a current of '$$I$$' ampere in one of the coils is brought to zero in '$$t$$' second, the e. m. f. induced per turn in the other coil in volt is