A balloon has mass of $$10 \mathrm{~g}$$ in air. The air escapes from the balloon at a uniform rate with velocity $$4.5 \mathrm{~cm} / \mathrm{s}$$. If the balloon shrinks in $$5 \mathrm{~s}$$ completely. Then, the average force acting on that balloon will be (in dyne).

If the radius of earth shrinks by $$2 \%$$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

The force required to stretch a wire of cross-section $$1 \mathrm{~cm}^{2}$$ to double its length will be : (Given Yong's modulus of the wire $$=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$$)

A Carnot engine has efficiency of $$50 \%$$. If the temperature of sink is reduced by $$40^{\circ} \mathrm{C}$$, its efficiency increases by $$30 \%$$. The temperature of the source will be: