Two blocks of masses \(m\) and \(M\) are connected by means of a metal wire of cross-sectional area \(A\) passing over a frictionless fixed pulley as shown in the figure. The system is then released. If \(M = 2\, m\), then the stress produced in the wire is

An artillery piece of mass \(M_1\) fires a shell of mass \(\mathrm{M}_2\) horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is _______.

Taking the wavelength of first Balmer line in hydrogen spectrum (\( n = 3\) to \(n = 2\) ) as \(660\,nm ,\) the wavelength of the \(2^{nd}\) Balmer line ( \(n =4\) to \(n = 2\) ) will be....\(nm\)

Distance of the centre of mass of a solid uniform cone from its vertex is \(z_0\) . If the radius of its base is \(R\) and its height is \(h\) then \(z_0\) is equal to

Let \(\vec A\, = \,(\hat i\, + \,\hat j)\,\)  and \(\vec B\, = \,(2\hat i\, - \,\hat j)\,.\)  The magnitude of a coplanar vector \(\vec C\) such that  \(\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B\) is given by

Two resistance of \(100\ \Omega\) and \(200\  \Omega\) are connected in series with a battery of \(4 \mathrm{~V}\) and negligible internal resistance. \(A\) voltmeter is used to measure voltage across \(100 \Omega\) resistance, which gives reading as \(1 \mathrm{~V}\). The resistance of voltmeter must be _______ \(\Omega\).

If \(B\) is magnetic field and \(\mu_0\) is permeability of free space, then the dimensions of \(\left(B / \mu_0\right)\) is

In the following circuit, the battery has an emf of \(2\mathrm{V}\) and an internal resistance of \(\frac{2}{3}\  \Omega\). The power consumption in the entire circuit is _______ \(W\).

The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon \(= 7.36 \times 10^{22}\,kg,\) radius of the moon's orbit \(= 3 .8 \times 10^8\,m\) ).

An object of mass ' \(m\) ' initially at rest on a smooth horizontal plane starts moving under the action of force \(F=2 N\). In the process of its linear motion, the angle \(\theta\) (as shown in figure) between the direction of force and horizontal varies as \(\theta= kx\), where \(k\) is a constant and \(x\) is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be \(E =\frac{ n }{ k } \sin \theta\). The value of \(n\) is \(.....\)

If electronic charge \(e\), electron mass \(m\), speed of light in vacuum \(c\) and Planck 's constant \(h\) are taken as fundamental quantities, the permeability of vacuum \(\mu _0\) can be expressed in units of

A person standing on a spring balance inside a stationary lift measures \(60 \,kg\). The weight of that person if the lift descends with uniform downward acceleration of \(1.8\, m / s ^{2}\) will be \(_{-} N\). \(\left[ g =10\, m / s ^{2}\right]\)