The ratio of de Broglie wavelength of a deutron with kinetic energy \(E\) to that of an alpha particle with kinetic energy \(2 E\), is \(n: 1\). The value of \(n\) is ___________.
(Assume mass of proton = mass of neutron) :

The charge accumulated on the capacitor connected in the following circuit is________ \(\mu \mathrm{C}\) (Given \(\mathrm{C}=150\  \mu \mathrm{F}\))

A spherical drop of liquid splits into \(1000\) identical spherical drops. If \(u _{ i }\) is the surface energy of the original drop and \(u_f\) is the total surface energy of the resulting drops, the (ignoring evaporation). \(\frac{u_f}{u_i}=\left(\frac{10}{x}\right)\). Then value of \(x\) is \(......\)

Two sources of light emit with a power of \(200 \mathrm{~W}\). The ratio of number of photons of visible light emitted by each source having wavelengths \(300\  \mathrm{nm}\) and \(500 \mathrm{~nm}\) respectively, will be _______.

The position vector of a particle changes with time according to the relation \(\vec r\left( t \right) = 15{t^2}\hat i + \left( {4 - 20{t^2}} \right)\hat j\). What is the magnitude of the acceleration at \(t = 1\) ?

When radiation of wavelength \(\lambda\) is used to illuminate a metallic surface, the stopping potential is \(V.\) When the same surface is illuminated with radiation of wavelength \(3 \lambda,\) the stopping potential is \(\frac{ V }{4} .\) If the threshold wavelength for the metallic surface is \(n \lambda\) then value of \(n\) will be......

A particle of mass \(m\) is moving with speed \(2\, v\) collides with a mass \(2\,m\) moving with speed \(v\) in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass \(m\), which move at angle \(45^o\) with respect to the original direction. The speed of each of the moving particle will be

Consider two blocks A and B of masses \(m_1=10 \mathrm{~kg}\) and \(m_2=5 \mathrm{~kg}\) that are placed on a frictionless table. The block A moves with a constant speed \(v=3 \mathrm{~m} / \mathrm{s}\) towards the block B kept at rest. A spring with spring constant \(\mathrm{k}=3000 \mathrm{~N} / \mathrm{m}\) is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is _______. (Neglect the mass of the spring)

A long, straight wire of radius \(a\) carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance \(\frac{a}{3}\) and \(2 a,\) respectively from the axis of the wire is

Two liquids of densities \(\rho_{1}\) and \(\rho_{2}\left(\rho_{2}=2 \rho_{1}\right)\) are filled up behind a square wall of side \(10\; \mathrm{m}\) as shown in figure. Each liquid has a height of \(5 \;\mathrm{m} .\) The ratio of the forces due to these liquids exerted on upper part \(MN\) to that at the lower pait \(NO\) is (Assume that the liquids are not mixing)

Two metal plates \((A, B)\) are kept horizontally with separation of \(\left(\dfrac{12}{\pi}\right)\) cm, with plate A on the top. An atomizer jet sprays oil (density \(1.5\) g/cm\(^3\)) droplets of radius \(1\) mm horizontally. All oil droplets carry a charge \(5\) nC. The potentials \(V_A\) and \(V_B\) are required on plates A and B respectively in order to ensure the droplets do not descend. The values of \(V_A\) and \(V_B\) are _______.
(Neglect the air resistance to the droplets and take \(g = 10\) m/s\(^2\))

In Young's double slit experiment, the distance between slits and the screen is \(1 .0\,\,m\) and monochromatic light of \(600\,\,nm\)  is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance \(d_0\) between the slits . If the angular resolution of the eye is \(\frac {1}{60}^o,\) the value of \(d_0\)  is close to......\(mm\)