What is the maximum value of the force $F$ such that the block shown in the arrangement does not move (in $N$)? (Take $g = 10 \ m/s^2$)

Assertion $(A)$: $A$ particle of mass $m$ dropped into a hole made along the diameter of the Earth from one end to the other executes simple harmonic motion.
Reason $(R)$: Gravitational force between any two particles is inversely proportional to the square of the distance between them.

The minimum force required to move a body up an inclined plane is three times the minimum force required to prevent it from sliding down the plane. If the coefficient of friction between the body and the inclined plane is $\frac{1}{2 \sqrt{3}}$,then the angle of the inclined plane is (in $^{\circ}$)

$1\, g$ of hydrogen is converted into $0.993\, g$ of helium in a thermonuclear reaction. The energy released is

Which of the following is a microbial insecticide?

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while box $B$ contains one mole of helium at temperature $(7/3) T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (Ignore the heat capacity of boxes). Then,the final temperature of gases,$T_f$,in terms of $T_0$ is