A ball having kinetic energy KE, is projected at an angle of \(60^{\circ}\) from the horizontal. What will be the kinetic energy of ball at the highest point of its flight ?

A gas mixture consists of \(8\) moles of argon and \(6\) moles of oxygen at temperature \(T\). Neglecting all vibrational modes, the total internal energy of the system is _______.

The electric field in a plane electromagnetic wave is given by \(\overrightarrow{{E}}=200 \cos \left[\left(\frac{0.5 \times 10^{3}}{{m}}\right) {x}-\left(1.5 \times 10^{11} \frac{{rad}}{{s}} \times {t}\right)\right] \frac{{V}}{{m}} \hat{{j}}\) If this wave falls normally on a perfectly reflecting surface having an area of \(100 \;{cm}^{2}\). If the radiation pressure exerted by the \(E.M.\) wave on the surface during a \(10\, minute\) exposure is \(\frac{{x}}{10^{9}} \frac{{N}}{{m}^{2}}\). Find the value of \({x}\).

A new unit \((\alpha)\) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of \(\alpha\) units if light takes \(6\) min. \(40\) s to cover this distance?

A block of mass 25 kg is pulled along a horizontal surface by a force at an angle \(45^{\circ}\) with the horizontal. The friction coefficient between the block and the surface is 0.25. The displacement of 5 m of the block is:

A constant magnetic field of \(1 \,{T}\) is applied in the \({x}\,>\,0\) region. A metallic circular ring of radius \(1 \,{m}\) is moving with a constant velocity of \(1 \,{m} / {s}\) along the \(x\)-axis. At \(t=0\) \(s,\) the centre of \(O\) of the ring is at \({x}=-1 \,{m}\). What will be the value of the induced \(emf\) in the ring at \(t=1\, s\) ? (Assume the velocity of the ring does not change.) (In \({V}\))

The change in the magnitude of the volume of an ideal gas when a small additional pressure \(\Delta P\) is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity \(\Delta T\) at constant pressure. The initial temperature and pressure of the gas were \(300\, K\) and \(2\; atm\) respectively. If \(|\Delta T|=C|\Delta P|\) then value of \(C\) in \((K / a t m)\) is......

The equivalent resistance between \(A\) and \(B\) is \(......\)

A heavy ball of mass \(M\) is suspended from the ceiling of car by a light string of mass \(m (m << M)\). When the car is at rest, the speed of transverse waves in the string is \(60\, ms^{-1}\). When the car has acceleration \(a\) , the wave-speed increases to \(60.5\, ms^{-1}\). The value of \(a\) , in terms of gravitational acceleration \(g\) is closest to

Three identical resistors with resistance \(R=12 \Omega\) and two identical inductors with sell inductance \(L=5 mH\) are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _________ A.

In an experment ot verify Newton's law of cooling, a graph is plotted between, the temperature difference \((\Delta T )\) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as \(80^{\circ} \,C\). The value of \(t _{2}\) as mentioned in the graph will be...........