Electric potential at a point \(P\) due to a point charge of \(5 \times 10^{-9}\; C\) is \(50 \;V\). The distance of \(P\) from the point charge is ......... \(cm\) (Assume, \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^{+9}\; Nm ^2 C ^{-2}\))

Three bodies \(A, B\) and \(C\) have equal kinetic energies and their masses are \(400 \mathrm{~g}, 1.2 \mathrm{~kg}\) and \(1.6 \mathrm{~kg}\) respectively. The ratio of their linear momenta is _______.

A body cools from \(60^{\circ} C\) to \(40^{\circ} C\) in \(6\) minutes. If, temperature of surroundings is \(10^{\circ} C\). Then, after the next 6 minutes, its temperature will be \(.........{ }^{\circ} C\).

12 wires each having resistance \(2 \Omega\) are joined to form a cube. A battery of \(6 \mathrm{~V}\) emf is joined across point \(\mathrm{a}\) and \(\mathrm{c}\). The voltage difference between \(e\) and \(f\) is ______V.

A short bar magnet placed with its axis at \(30^{\circ}\) with an external field of 800 Gauss, experiences a torque of \(0.016 N . m\). The work done in moving it from most stable to most unstable position is \(\alpha \times 10^{-3} J\). The value of \(\alpha\) is _________ .

Space between the plates of a parallel plate capacitor of plate area \(4 \mathrm{~cm}^2\) and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ________ pF. \(\left(\right.\) Given \(\left.\varepsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\)

A pendulum is suspended by a string of length \(250\,cm\). The mass of the bob of the pendulum is \(200\,g\). The bob is pulled aside until the string is at \(60^{\circ}\) with vertical as shown in the figure. After releasing the bob. the maximum velocity attained by the bob will be________ \(ms ^{-1}\). (if \(g=10\,m / s ^{2}\) )

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
\(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right) V / m\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is __________ .
(speed of light in free space is \(3 \times 10^8 m / s\) )

Unpolarized light of intensity \(I_0\) incident on surface of a block of glass at Brewster's angle. In that case, which one of ihe following statements is true ?

The surface tension of soap solution is \(3.5 \times 10^{-2}\,Nm ^{-1}\). The amount of work done required to increase the radius of soap bubble from \(10\,cm\) to \(20\,cm\) is \(.....\times 10^{-4}\,J\)

A travelling microscope is used to determine the refractive index of a glass slab. If \(40\) divisions are there in \(1 \; cm\) on main scale and \(50\) Vernier scale divisions are equal to \(49\) main scale divisions, then least count of the travelling microscope is \(\dots \; \times 10^{-6} \; m\)

A student determined Young's Modulus of elasticity using the formula \(Y=\frac{M g L^{3}}{4 b d^{3} \delta} .\) The value of \(g\) is taken to be \(9.8 \,{m} / {s}^{2}\), without any significant error, his observation are as following.

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass \(({M})\)	\(1\; {g}\)	\(2\; {kg}\)
Length of bar \((L)\)	\(1\; {mm}\)	\(1 \;{m}\)
Breadth of bar \((b)\)	\(0.1\; {mm}\)	\(4\; {cm}\)
Thickness of bar \((d)\)	\(0.01\; {mm}\)	\(0.4 \;{cm}\)
Depression \((\delta)\)	\(0.01\; {mm}\)	\(5 \;{mm}\)

Then the fractional error in the measurement of \({Y}\) is