In a uniform magnetic field of $$0.049 \mathrm{~T}$$, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $$9.8 \times 10^{-6} \mathrm{~kg} \mathrm{~m}^2$$. If the magnitude of magnetic moment of the needle is $$x \times 10^{-5} \mathrm{~Am}^2$$, then the value of '$$x$$' is :
A wire of length '$$l$$' and resistance $$100 \Omega$$ is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:
A horizontal force $$10 \mathrm{~N}$$ is applied to a block $$A$$ as shown in figure. The mass of blocks $$A$$ and $$B$$ are $$2 \mathrm{~kg}$$ and 3 $$\mathrm{kg}$$ respectively. The blocks slide over a frictionless surface. The force exerted by block $$A$$ on block $$B$$ is :
A tightly wound 100 turns coil of radius $$10 \mathrm{~cm}$$ carries a current of $$7 \mathrm{~A}$$. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $$4 \pi \times 10^{-7} \mathrm{SI}$$ units):