A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be \(......km\) (Take radius of earth \(=6400\,km\) and \(g =10\,ms^{-2}\) )

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be \(t_1\) and \(t_2\), respectively, then...

The time taken by an object to slide down \(45^{\circ}\) rough inclined plane is \(n\) times as it takes to slide down a perfectly smooth \(45^{\circ}\) incline plane. The coefficient of kinetic friction between the object and the incline plane is

In the circuit shown, the energy stored in the capacitor is \(n\,\mu J\). The value of \(n\) is ..............

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ___________.
(Given: \(h=6.63\times10^{-34}\) J.s and \(c=3\times10^{8}m/s\))

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

A common example of alpha decay is \({ }_{82}^{238} U \longrightarrow{ }_{80}^{234} Th +{ }_2 He ^4+ Q\).  ( Given : \({ }_{92}^{238} U =238.05060 u ,\) \({ }_{90}^{234} Th =234.04360 u ,\) \({ }_2^4 He =4.00260 u \text {, and }\) \(1 u =931.5 \frac{ MeV }{ c ^2} )\). The energy released \((Q)\) during the alpha decay of \({ }_{92}^{238} U\) is \(......\,MeV\)

The following bodies, \((1)\) a ring \((2)\) a disc \((3)\) a solid cylinder \((4)\) a solid sphere, of same mass \(m\) and radius \(R\) are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ........... [Mark the body as per their respective numbering given in the question]

The function of time representing a simple harmonic motion with a period of \(\frac{\pi}{\omega}\) is :

The threshold frequency of a metal with work function \(6.63\  \mathrm{eV}\) is:

In single slit diffraction pattern, the wavelength of light used is \(628\) nm and slit width is \(0.2\) mm, the angular width of central maximum is \(\alpha \times 10^{-2}\) degrees. The value of \(\alpha\) is _______.

The ratio of surface tensions of mercury and water is given to be \(7.5\) while the ratio of their densities is \(13.6\). Their contact angles, with glass, are close to \(135^o\) and \(0^o\), respectively. It is observed that mercury gets depressed by an amount \(h\) in a capillary tube of radius \(r_1\), while water rises by the same amount \(h\) in a capillary tube of radius \(r_2\). The ratio, \((r_1/r_2)\), is then close to

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is \(\left(\frac{a-1}{a}\right)\) then the value of \(a\) is _______.