Consider the reacting at $300K$
$C_6{H}_6\left(l\right)+\frac{15}{2}{O}_2\left(l\right)\to 6C{O}_2\left(g\right)+3H_{2}O\left(l\right),\Delta H=-3271kJ$
What is $\Delta U$ for the combustion of $1.5$ mole of benzene at ${27}^{\circ }C$ ?

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is

A rubber ball drops from a height 'h'. After rebounding twice from the ground, it rises to $h/2.$ The co-efficient of restitution is

From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure Taking gravitational potential $V=0atr=\infty$, the potential at (G = gravitational constatn)

A ball of mass $m$ is projected with a velocity ${}^{\prime }{u}^{\prime }$ at angle $\theta$ with the horizontal. It collides with a smooth box of mass ${}^{\prime }{M}^{\prime }$ at its highest position. If the co-efficient of restitution is ${}^{\prime }{e}^{\prime }.$

Find the position at which the ball meets the x-axis from the origin

A string is cut into three parts, having fundamental frequencies $n_1,n_2$ and $n_3$ respectively. Then original fundamental frequency 'n' related by the expression as (other quantities are identical) :-

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the cirucmferences of the discs coincide. The centre of mass of the new disc is $\frac{\alpha }{R}$ from the center of the bigger disc. The value of $\alpha$ is

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction when the angle of inclination of the plane is ${60}^{\circ }$ is .

A sphere of mass $m$ moving with constant velocity $u$, collides with another stationary sphere of same mass. If $e$ is the coefficient of restitution, the ratio of the final velocities of the first and second sphere is

A ball of mass $10kg$ strikes another ball of mass $25kg$ at rest. If they separated in mutually perpendicular directions then the coefficient of restitution is: