A body rolls down an inclined plane without slipping. The kinetic energy of rotation is \(50 \,\%\) of its translational kinetic energy. The body is :

The velocity of a small ball of mass \(0.3\,g\) and density \(8\,g / cc\) when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(1.3\,g / cc\), then the value of viscous force acting on the ball will be \(x \times 10^{-4}\,N\), the value of \(x\) is [use \(g=10\,m / s ^{2}\) ] 

A rod of length \(10\) cm lies along the principle axis of a concave mirror of focal length \(10\) cm as shown in figure. The length of the image is _____ cm.

A radioactive element \({ }_{92}^{242} X\) emits two \(\alpha\)-particles, one electron and two positrons. The product nucleus is represented by \({ }_{ P }^{234} Y\). The value of \(P\) is \(..................\)

The \(rms\) speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are \({V}_{{H}}, {V}_{0}\) and \({V}_{{C}}\) respectively then

Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential

A galvanometer has a resistance of \(50 \Omega\) and allows a maximum current of \(5 \mathrm{~mA}\) to pass. What is the necessary series resistance to connect to convert it to a voltmeter that can measure \(100 \mathrm{~V}\)?

A particle of mass \(2\, kg\) is moving such that at time \(t\), its position, in meter, is given by \(\overrightarrow r \left( t \right) = 5\hat i - 2{t^2}\hat j\) . The angular momentum of the particle at \(t\, = 2\, s\) about the origin in \(kg\, m^{-2}\, s^{-1}\) is

An insulated copper wire of \(100\) turns is wrapped around a wooden cylindrical core of the crosssectional area \(24\,cm ^2\). The two ends of the wire are connected to a resistor. The total resistance in the circuit is \(12\,\Omega\). If an externally applied uniform magnetic field in the core along its axis changes from \(1.5 T\) in one direction to \(1.5\,T\) in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be \(.........\,mC\).

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity \(K _{1}, K _{2},\) and \(K _{3}\), respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at \(100^{\circ} C\) and the ther at \(0^{\circ} C\) (see figure). If the joints of the rod are at  \(70^{\circ} C\) and \(20^{\circ} C\) in steady state and there is no loss of energy from the surface of the rod, the correct relationship between \(K _{1}, K _{2}\) and \(K _{3}\) is