If the temperature of a hot body is increased by $$50 \%$$, then the increase in the quantity of emitted heat radiation will be approximately

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '$$L$$'. The length of the open pipe will be

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