A particle moving with kinetic energy \(E\) has de Broglie wavelength \(\lambda\). If energy \(\Delta \mathrm{E}\) is added to its energy, the wavelength become \(\frac {\lambda}{2} .\) Value of \(\Delta \mathrm{E},\) is 

A small cube of side \(1\) mm is placed at the centre of a circular loop of radius \(10\) cm carrying a current of \(2\) A. The magnetic energy stored inside the cube is \(\alpha \times 10^{-14}\) J. The value of \(\alpha\) is _______. (\(\mu_o = 4\pi \times 10^{-7}\) Tm/A, \(\pi = 3.14\))

A simple pendulum is being used to determine the value of gravitational acceleration \(\mathrm{g}\) at a certain place. The length of the pendulum is \(25.0\; \mathrm{cm}\) and a stop watch with \(1\; \mathrm{s}\) resolution measures the time taken for \(40\) oscillations to be \(50\; s\). The accuracy in \(g\) is  ....... \(\%\)

An \(n-p-n\) transistor has three leads \(A,B\) and \(C\) . Connecting \(B\) and \(C\) by moist fingers, \(A\) to the positive lead of an ammeter, and \(C\) to the negative lead of the ammeter, one finds large deflection. Then, \(A, B\) and \(C\) refer respectivily to

A wire of resistance \(20 \Omega\) is divided into \(10\) equal parts. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is _______\(\Omega\).

Find the magnetic field at point \(P\) due to a straight line segment \(AB\) of length \(6\, cm\) carrying a current of \(5\, A\). (See figure) \((\mu _0 = 4p\times10^{-7}\, N-A^{-2})\)

A radioactive substance decays to \(\left(\frac{1}{16}\right)^{t h}\) of its initial activity in \(80\, days.\) The half life of the radioactive substance expressed in days is ... .

A null point is found at \(200\,cm\) in potentiometer when cell in secondary circuit is shunted by \(5\,\Omega\). When a resistance of \(15\,\Omega\) is used for shunting null point moves to \(300\,cm\). The internal resistance of the cell is \(..............\,\Omega\).

Given below are two statements: Statement\(-I :\) An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement\(-II :\) Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below :

At the centre of a half ring of radius \(R=10 \mathrm{~cm}\) and linear charge density \(4 \mathrm{n} \mathrm{C} \mathrm{m}^{-1}\), the potential is \(x \pi V\). The value of \(x\) is _______.

The velocity of a particle executing simple harmonic motion along \(x\)-axis is described as \(v^2 = 50 - x^2\), where \(x\) represents displacement. If the time period of motion is \(\dfrac{x}{7}\) s, the value of \(x\) is _____.