A magnetic needle is kept in a non-uniform magnetic field. It experiences :

A particle of mass $$10$$ $$g$$ is kept on the surface of a uniform sphere of mass $$100$$ $$kg$$ and radius $$10$$ $$cm.$$ Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $$G$$ $$=6.67\times 10^{-11}N{m}^2/k{g}^2$$)

The change in the value of $$g$$ at a height $$h$$ above the surface of the earth is the same as at a depth $$d$$ below the surface of earth. When both $$d$$ and $$h$$ are much smaller than the radius of earth, then which one of the following is correct?

Average density of the earth

Two point white dots are $$1$$ $$mm$$ apart on a black paper. They are viewed by eye of pupil diameter $$3$$ $$mm.$$ Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light $$=500$$ $$nm$$ ]

A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

If $$I_0$$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

When an unpolarized light of intensity $$I_0$$ is incident on a polarizing sheet, the intensity of the light which does not get transmitted is

A parallel plate capacitor is made by stacking $$n$$ equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is $${}^{\prime }{C}^{\prime }$$ then the resultant capacitance is

A fully charged capacitor has a capacitance $${}^{\prime }{C}^{\prime }$$. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity $${}^{\prime }{s}^{\prime }$$ and mass $${}^{\prime }{m}^{\prime }.$$ If the temperature of the block is raised by $${}^{\prime }\Delta T^{\prime },$$ the potential difference $${}^{\prime }{v}^{\prime }$$ across the capacitance is

When two tuning forks (fork $$1$$ and fork $$2$$) are sounded simultaneously, $$4$$ beats per second are heated. Now, some tape is attached on the prong of the fork $$2.$$ When the tuning forks are sounded again, $$6$$ beats per second are heard. If the frequency of fork $$1$$ is $$200$$ $$Hz$$, then what was the original frequency of fork $$2$$ ?

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency ?

Two thin, long, parallel wires, separated by a distance $${}^{\prime }{d}^{\prime }$$ carry a current of $${}^{\prime }{i}^{\prime }$$ $$A$$ in the same direction. They will

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then

Two concentric coils each of radius equal to $$2$$ $$\pi$$ $$cm$$ are placed at right angles to each other. $$3$$ ampere and $$4$$ ampere are the currents flowing in each coil respectively . The magnetic induction in Weber / $$m^2$$ at the center of the coils will be $$\left(\mu =4\pi \times {10}^{-7}Wb/A.m\right)$$

A charged particle of mass $$m$$ and charge $$q$$ travels on a circular path of radius $$r$$ that is perpendicular to a magnetic field $$B.$$ The time taken by the particle to complete one revolution is

A particle of mass 0.3 kg subjected to a force $$F=-kx$$ with $$k=15$$ $$N/m$$. What will be its initial acceleration if it is released from a point 20 cm away from the origin?

A smooth block is released at rest on a $$45^{\circ }$$ incline and then slides a distance $${}^{\prime }{d}^{\prime }$$. The time taken to slide is $${}^{\prime }{n}^{\prime }$$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A block is kept on a frictionless inclined surface with angle of inclination $${}^{\prime }\alpha {}^{\prime }.$$ The incline is given an acceleration $$a$$ to keep the block stationary. Then $$a$$ is equal to

Consider a car moving on a straight road with a speed of $$100$$ $$m/s$$. The distance at which car can be stopped is $$\left[{\mu }_k=0.5\right]$$