Physics

A hollow spherical shell at outer radius $\mathrm{R}$ floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is $\frac{27}{8}$ w.r.t water, the value of r is.

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is $$ $30\mathrm{c}\mathrm{m}$ and the refractive index of the lens material is 1.5 , then the focal length of the lens (in $\mathrm{c}\mathrm{m}$ $$ ) is(Ray Optics)

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300\mathrm{m}/\mathrm{s}$ $$ , the frequency difference between the fundamental and second harmonic of this pipe is $\mathrm{H}\mathrm{z}$ $$

A body $A$ $$ , of mass $m=0.1\mathrm{k}\mathrm{g}$ $$ has an initial velocity of $3\hat{i}{\mathrm{m}\mathrm{s}}^{-1}$ $\stackrel{}{}{}^{}$ . It collides elastically with another body, $B$ $$ of the same mass which has an initial velocity of $5\hat{j}{\mathrm{m}\mathrm{s}}^{-1}$ $\stackrel{}{}{}^{}$ . After collision, A moves with a velocity $\stackrel{?}{v}=4(\hat{i}+\hat{j})$ $\stackrel{}{}\stackrel{}{}\stackrel{}{}$ . The energy of $$ $B$ after collision is written as $\frac{}{}$ $\frac{x}{10}\mathrm{J}$ . The value of $x$ $$ is

A particle is moving along the $x$ $$ -axis with its coordinate with time ' $t$ $$ ' given by $x\left(t\right)=10+8t-3t^2$ ${}^{}$ . Another particle is moving along the $$ $y$ -axis with its coordinate a function of time given by $y\left(t\right)=5-8t^3$ ${}^{}$ . At $t=1\mathrm{s}$ $$ , the speed of the second particle as measured in the frame of the first particle is given as $\sqrt[]{v}$ $\text{exception 25:}$ . Then $v$ $$ (in $$ ) $\mathrm{m}/\mathrm{s}$ is

Four resistances of $15\mathrm{\Omega },12\mathrm{\Omega },4\mathrm{\Omega }$ $$ and $$ $10\mathrm{\Omega }$ respectively in cyclic order to form Whetstone's network. The resistance that is to be connected in parallel with the resistance of $10\mathrm{\Omega }$  to balance the network is

Consider two solid spheres of radii ${}_{}$ $R_1=1\mathrm{m}$ , $R_2=2m$ ${}_{}$ and masses $M_1$ ${}_{}$ and $M_2$ ${}_{}$ , respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $\frac{M_1}{M_2}$ $\frac{{}_{}}{{}_{}}$ is:

Consider two solid spheres of radii $R_1=1\mathrm{m}$ ${}_{}$ , $R_2=2m$ ${}_{}$ and masses $M_1$ ${}_{}$ and $M_2$ ${}_{}$ , respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $\frac{M_1}{M_2}$ $\frac{{}_{}}{{}_{}}$ is:

Three charged particles $A,B$ $$ and $C$ $$ with charges $-4q,2q$ $$ and $$ $-2q$  are present on the circumference of a circle of radius $d$ $$ . The charged particles $A,C$ $$ and centre $O$ $$ of the circle formed an equilateral triangle as shown in figure. Electric field at $\mathrm{O}$ $$ along $\mathrm{x}$ $$ -direction is:

A leak proof cylinder of length $1\mathrm{m}$ $$ , made of a metal which has very low coefficient of expansion is floating vertically in water at $0^{?}\mathrm{C}$ ${}^{}$ such that its height above the water surface is $20\mathrm{c}\mathrm{m}$ $$ . When the temperature of water is increased to $4^{?}\mathrm{C}$ ${}^{}$ , the height of the cylinder above the water surface becomes $$ $21\mathrm{c}\mathrm{m}$ . The density of water at $\mathrm{T}=4^{?}\mathrm{C}$ ${}^{}$ , relative to the density at $\mathrm{T}=0^{?}\mathrm{C}$ ${}^{}$ is close to: