Two waves $Y_1 = 0.25 \sin 316 t$ and $Y_2 = 0.25 \sin 310 t$ are propagating in the same direction. The number of beats produced per second is

$A$ ray of light passes through an equilateral prism $(\mu = 1.5)$ such that the angle of incidence is equal to the angle of emergence,and the latter is equal to $3/4$ of the prism angle. The angle of deviation is....$^o$

When a spring is stretched by $2 \ cm$,it stores $100 \ J$ of energy. If it is stretched further by $2 \ cm$,the stored energy will be increased by ............. $J$.

$ICBN$ stands for

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

The two surfaces of a biconvex lens have the same radii of curvature. This lens is made of glass with a refractive index of $1.5$ and has a focal length of $10 ~cm$ in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. The two pieces are glued such that the convex surfaces touch each other. If this combination lens is immersed in water (refractive index $=$ $4/3$),its focal length (in $cm$) is: