The work done by a force $\vec F = (-6x^3 \hat i) \text{ N}$,in displacing a particle from $x = 4 \text{ m}$ to $x = -2 \text{ m}$ is .............. $J$.

$A$ $500 \,\mu F$ capacitor is charged at a steady rate of $100\, \mu C/s$. The potential difference across the capacitor will be $10\, V$ after an interval of.....$s$.

The equation of the tangent to the curve $6y = 7 - x^3$ at the point $(1, 1)$ is:

When a body of mass $1.0 ~kg$ is suspended from a certain light spring hanging vertically,its length increases by $5 ~cm$. By suspending a $2.0 ~kg$ block to the spring,if the block is pulled through $10 ~cm$ and released,the maximum velocity in $m/s$ is: (Acceleration due to gravity $= 10 ~m/s^2$)

The velocity of a particle which starts from rest is given by the following table. The total distance travelled (in metre) by the particle in $10 \ s$,using the Trapezoidal rule is given by:

$t$ (in second)	$0$	$2$	$4$	$6$	$8$	$10$
$v$ (in m/s)	$0$	$12$	$16$	$20$	$35$	$60$

Three samples of the same gas $A, B$ and $C$ $(\gamma = 3/2)$ initially have equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$,isobaric for $B$ and isothermal for $C$. If the final pressures are equal for all three samples,the ratio of their initial pressures is: