A cyclotron is used to accelerate protons. If the operating magnetic field is $1.0 \mathrm{T}$ and the radius of the cyclotron 'dees' is $60 \mathrm{cm}$, the kinetic energy of the accelerated protons in $\mathrm{MeV}$ will be :
[use $m_{\mathrm{p}}=1.6\times {10}^{-27} \mathrm{kg}, e=1.6\times {10}^{-19} \mathrm{C}$]

The current sensitivity of a galvanometer can be increased by :
(A) decreasing the number of turns
(B) increasing the magnetic field
(C) decreasing the area of the coil
(D) decreasing the torsional constant of the spring

Choose the most appropriate answer from the options given below :

As shown in the figure, a metallic rod of linear density $0.45 \mathrm{kg}{ \mathrm{m}}^{-1}$ is lying horizontally on a smooth incline plane which makes an angle of $45°$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $0.15 \mathrm{T}$ magnetic field is acting on it in the vertically upward direction, will be

(Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A triangular shaped wire carrying $10 \mathrm{A}$ current is placed in a uniform magnetic field of $0.5 \mathrm{T}$, as shown in figure. The magnetic force on segment $CD$ is (Given $BC=CD=BD=5 \mathrm{cm}$).

A wire $X$ of length $50 \mathrm{cm}$ carrying a current of $2 \mathrm{A}$ is placed parallel to a long wire $Y$ of length $5 \mathrm{m}$. The wire $Y$ carries a current of $3 \mathrm{A}$. The distance between two wires is $5 \mathrm{cm}$ and currents flow in the same direction. The force acting on the wire $Y$ is :

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