$A$ satellite is launched into a circular orbit of radius $R$ around the Earth,while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is:

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300 \ K$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30 \ K$,then the rise in temperature of the gas in $B$ is ..... $K$

If $Z_r = \cos \left(\frac{\pi}{2^r}\right) + i \sin \left(\frac{\pi}{2^r}\right)$ for $r = 1, 2, 3, \ldots$,then the product $Z_1 Z_2 Z_3 \ldots \infty$ is equal to:

The figure shows the variation of $R$,$X_L$,and $X_C$ with frequency $f$ in a series $LCR$ circuit. For which frequency point is the circuit inductive?

The reaction $X \rightarrow \text{products}$ is a first order reaction. In $40 \text{ minutes}$,the concentration of $X$ changes from $1.0 \text{ M}$ to $0.25 \text{ M}$. What is the rate of reaction when $[X] = 0.1 \text{ M}$? $(\log 4 = 0.60)$

Two lithium nuclei in a lithium vapour at room temperature do not combine to form a carbon nucleus because