The speed of electrons in a scanning electron microscope is \(1 \times 10^{7} \,ms ^{-1}\). If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of:

The orbital angular momentum of a satellite is \(L\), when it is revolving in a circular orbit at height \(h\) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be \(............\,L\)

In a circuit for finding the resistance of a galvanometer by half deflection method, a  \(6\,V\)  battery and a high resistance of  \(11\,k\Omega \)  are used. The figure of merit of the galvanometer \(60\,\mu A/\)  division. In the absence of shunt resistance, the galvanometer produces a deflection of  \(\theta = 9\)  divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of \(\theta /2 ,\)  is closest to ..................  \(\Omega\)

A beam of unpolarised light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^o \) relative to that of \(A\). The intensity of the emergent light is _______.

A capacitor of \(50 \,\mu {F}\) is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is \(......\,\mu {C} .\)

A wire of length \(L\) and radius \(r\) is clamped at one end. If its other end is pulled by a force \(F\), its length increases by \(l\). If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become _______.

A proton with a kinetic energy of \(2.0\,eV\) moves into a region of uniform magnetic field of magnitude \(\frac{\pi}{2} \times 10^{-3}\,T\). The angle between the direction of magnetic field and velocity of proton is \(60^{\circ}\). The pitch of the helical path taken by the proton is \(..........cm\) (Take, mass of proton \(=1.6 \times 10^{-27}\,kg\) and Charge on proton \(=1.6 \times 10^{-19}\,kg)\)

The maximum rated power of the LED is \(2\) mW and it is used in the circuit with input voltage of \(5\) V as shown in the figure below. The current through resistance \(R_S\) is \(0.5\) mA. The minimum value of the resistance of \(R_S\), to ensure that the LED is not damaged is _______ k\(\Omega\).

There are two long co -axial solenoids of same length \(l.\) The inner and outer coils have radii \(r_1\) and \(r_2\) and number of turns per unit length \(n_1\) and \(n_2\) respectively. The ratio of mutual inductance to the self -inductance of the inner -coil is

A capacitor is made of a tlat plate of area \(A\) and a second plate having a stair-like structure as shown in figure. If the area of each stair is \(\frac{A}{3}\) and the height is \(\mathrm{d}\), the capacitance of the arrangement is _______.

The speed of light in media \('A'\) and \('B'\) are \(2.0 \times\) \(10^{10} \,cm / s\) and \(1.5 \times 10^{10} \,cm / s\) respectively. A ray of light enters from the medium \(B\) to \(A\) at an incident angle ' \(\theta\) '. If the ray suffers total internal reflection, then

Identify the pair of physical quantities that have same dimensions