Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth \(d=\frac{R}{2}\) from the surface of earth, if its werght on the surface of earth is \(200\,N\), will be \(...........\,N\) ( \(Given R =\) Radrus of earth)

Four identical rectangular plates with length, \(l=2\, cm\) and breadth, \(b =\frac{3}{2}\, cm\) are arranged as shown in figure. The equivalent capacitance between \(A\) and \(C\) is \(\frac{ x \varepsilon_{0}}{ d } .\) The value of \(x\) is (Round off to the Nearest Integer)

A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants \(K_1, K_2, K_3, K_4\) arranged as shown in the figure. The effective dielectric constant \(K\) will be

Three different processes that can occur in an ideal monoatomic gas are shown in the \(P\) vs \(V\) diagram. The paths are labelled as \(A \rightarrow B, A \rightarrow C\) and \(A \rightarrow D .\) The change in internal energies during these process are taken as \(E _{ AB }, E _{ AC }\) and \(E _{ AD }\) and the work done as \(W _{ AB }\) \(W _{ AC }\) and \(W _{ AD }\) The correct relation between these parameters are

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant \(K\) is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \(\frac{3}{4} d\), where \('d'\) is the separation between the plates of parallel plate capacitor. The new capacitance \((C')\) in terms of original capacitance \(\left( C _{0}\right)\) is given by the following relation

A particle \(A\) of mass \(‘m’\) and charge \(‘q’\) is accelerated by a potential difference of \(50\, V\). Another particle \(B\) of mass \(‘4\, m’\) and charge \(‘q’\) is accelerated by a potential difference of \(2500\, V\). The ratio of de-Broglie wavelength \(\frac{{{\lambda _A}}}{{{\lambda _B}}}\) is close to

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as \(10\text{ V}\) and \(5\text{ A}\), respectively. The least counts of voltmeter and ammeter are \(500\text{ mV}\) and \(200\text{ mA}\), respectively. The estimated error in the resistance measurement is _______ \(\Omega\).

Two identical metallic spheres \(A\) and \(B\) when placed at certain distance in air repel each other with a force of \(F\). Another identical uncharged sphere \(C\) is first placed in contact with \(A\) and then in contact with \(B\) and finally placed at midpoint between spheres \(A\) and \(B\). The force experienced by sphere \(C\) will be.

An electron of mass \(m_{e}\) and a proton of mass \(m_{p}\) are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is

Five equal resistances are connected in a network as shown in figure. The net resistance between the points \(A\) and \(B\) is

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm , respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be _______.