A capacitor has air as dielectric medium and two conducting plates of area $$12{\mathrm{cm}}^2$$ and they are $$0.6\mathrm{cm}$$ apart. When a slab of dielectric having area $$12{\mathrm{cm}}^2$$ and $$0.6\mathrm{cm}$$ thickness is inserted between the plates, one of the conducting plates has to be moved by $$0.2\mathrm{cm}$$ to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given $${ϵ}_0=8.834\times 10^{-12}\mathrm{F}/\mathrm{m}$$)

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $$60\mathrm{cm}$$, the length of the closed pipe will be:

A plane progressive wave is given by $$y=2\cos 2\pi (330\mathrm{t}-x)\mathrm{m}$$. The frequency of the wave is :

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $$\overrightarrow{\mathrm{E}}$$ and $$\overrightarrow{\mathrm{B}}$$ represent the electric and magnetic fields respectively, then the region of space may have : (A) $$\mathrm{E}=0,\mathrm{B}=0$$ (B) $$\mathrm{E}=0,\mathrm{B}\ne 0$$ (C) $$\mathrm{E}\ne 0,\mathrm{B}=0$$ (D) $$\mathrm{E}\ne 0,\mathrm{B}\ne 0$$ Choose the most appropriate answer from the options given below :

A uniform magnetic field of $$2\times 10^{-3}\mathrm{T}$$ acts along positive $$Y$$-direction. A rectangular loop of sides $$20\mathrm{cm}$$ and $$10\mathrm{cm}$$ with current of $$5\mathrm{A}$$ is in $$Y-Z$$ plane. The current is in anticlockwise sense with reference to negative $$X$$ axis. Magnitude and direction of the torque is:

A rigid wire consists of a semicircular portion of radius $$R$$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $$B=B_0\hat{k}$$ as shown in figure. The magnetic force on the wire if it has a current $$i$$ is:

Two particles $$X$$ and $$Y$$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $$R_1$$ and $$R_2$$ respectively. The mass ratio of $$X$$ and $$Y$$ is :

Two insulated circular loop A and B of radius '$$a$$' carrying a current of '$$\mathrm{I}$$' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be :

A proton and a deutron $$(q=+\mathrm{e},m=2.0\mathrm{u})$$ having same kinetic energies enter a region of uniform magnetic field $$\vec{B}$$, moving perpendicular to $$\vec{B}$$. The ratio of the radius $$r_d$$ of deutron path to the radius $$r_p$$ of the proton path is:

Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below :

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $$\frac{a}{2}$$ and $$2a$$ from axis of the wire is :

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

The electrostatic force $$\left(\overrightarrow{F_1}\right)$$ and magnetic force $$\left({\vec{F}}_2\right)$$ acting on a charge $$q$$ moving with velocity $$v$$ can be written :

An element $$\Delta l=\Delta x\hat{i}$$ is placed at the origin and carries a large current $$I=10\mathrm{A}$$. The magnetic field on the $$y$$-axis at a distance of $$0.5\mathrm{m}$$ from the elements $$\Delta x$$ of $$1\mathrm{cm}$$ length is:

A body of mass $4\mathrm{kg}$ experiences two forces ${\vec{F}}_1=5\hat{i}+8\hat{j}+7\hat{k}$ and ${\overrightarrow{\mathrm{F}}}_2=3\hat{i}-4\hat{j}-3\hat{k}$. The acceleration acting on the body is :

A cricket player catches a ball of mass $120\mathrm{g}$ moving with $25\mathrm{m}/\mathrm{s}$ speed. If the catching process is completed in $0.1\mathrm{s}$ then the magnitude of force exerted by the ball on the hand of player will be (in SI unit) :

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04 , the acceleration of the system in ${\mathrm{ms}}^{-2}$ is : (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) :

Given below are two statements : Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials. Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below :

A block of mass $$5\mathrm{kg}$$ is placed on a rough inclined surface as shown in the figure. If $$\overrightarrow{F_1}$$ is the force required to just move the block up the inclined plane and $$\overrightarrow{F_2}$$ is the force required to just prevent the block from sliding down, then the value of $$\left|\overrightarrow{F_1}\right|-\left|\overrightarrow{F_2}\right|$$ is : [Use $$\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2]$$