A bag is gently dropped on a conveyor belt moving at a speed of \(2\,m / s\). The coefficient of friction between the conveyor belt and bag is \(0.4\) Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is \(.....m\) [Take \(g=10\,m / s ^{-2}\) ]

A ray of ligh is incident at an angle of incidence \(60^{\circ}\) on the glass slab of refractive index \(\sqrt{3}\). After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is \(4 \sqrt{3} \,cm\). The thickness of the glass slab is. . .  .. . \(cm\).

An \(\alpha\)-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength:

A paramagnetic material has \(10^{28}\,atoms/m^3.\) Its magnetic susceptibility at temperature \(350\,K\) is \(2.8 \times 10^{-4}.\) Its susceptibility at \(300\,K\) is

For the series LCR circuit connected with 220 V , 50 Hz a.c source as shown in the figure, the power factor is \(\frac{\alpha}{10}\). The value of \(\alpha\) is _________

If the screw on a screw-gauge is given six rotations, it moves by \(3\; \mathrm{mm}\) on the main scale. If there are \(50\) divisions on the circular scale the least count of the screw gauge is

A parallel plate capacitor is made of two plates of length \(l\), width \(w\) and separated by distance \(d\). A dielectric slab ( dielectric constant \(K\)) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force \(F = -\frac{{\partial U}}{{\partial x}}\) where \(U\) is the energy of the capacitor when dielectric is inside the capacitor up to distance \(x\) (See figure). If the charge on the capacitor is \(Q\) then the force on the dielectric when it is near the edge is

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at \(30^{\circ} C\). The coefficient of linear expansion of aluminium and steel are \(24 \times 10^{-6} /{ }^{\circ} C\) and \(1.2 \times 10^{-5} /{ }^{\circ} C\), respectively. The length of this composite rod when its temperature is raised to \(100^{\circ} C\), is _________ cm .

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)

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :- \(A.\) Real \(B.\) Erect \(C.\) Smaller in size then object \(D.\) Laterally inverted Choose the most appropriate answer from the options given below :

The current \((i)\) at time \(t =0\) and \(t =\infty\) respectively for the given circuit is