A solid sphere rolling without friction on a horizontal surface with a constant speed of $2 \mathrm{~m} / \mathrm{s}$, rolls up on an inclined ramp which is inclined at $30^{\circ}$. The maximum distance travelled by the sphere on the inclined ramp is (acceleration due to gravity $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sin 30^{\circ}=\frac{1}{2}$ )

In Young's double slit experiment with monochromatic light of wavelength 600 nm , the distance between the slits is $10^{-3} \mathrm{~m}$. For changing the fringe width by $3 \times 10^{-5} \mathrm{~m}$

a. the screen is moved away from the slit by 5 cm .

b. the screen is moved 5 cm towards the slits.

c. the screen is moved 3 cm towards the slits.

d. the screen is moved away from the slits by 3 cm .

An achromatic convergent doublet of two lenses in contact has a power +2 D . The convex lens has power +5 D . The ratio of the dispersive powers of the convergent and divergent lenses is (in magnitude)

Two bar magnets A and B are geometrically similar but the magnetic moment of $A$ is twice that of $B$. $T_1$ is the time period of oscillation when their like poles are kept together. When unlike poles are kept together, the time period of oscillation is $T_2$. The ratio $T_1: T_2$ will be