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:
Given below are two statements :
Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : The rms speed of oxygen molecules in a gas is $$v$$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $$2 v$$.
In the light of the above statements, choose the correct answer from the options given below :