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In a uranium reactor whose thermal power is $P=100\text{MW}.$ If the average number of neutrons liberated in each nuclear splitting is $2.5$ each splitting is assumed to release an energy $E=200\text{MeV}.$ The number of neutrons generated per unit time is

The magnetic flux $\varphi$ (in weber) linked with a coil of resistance 10$\Omega$ varies with time t (in second) as $\varphi$=8 $t^2$-4t+1.The current induced in the coil at is t=0.1 sec is

Find time t, when the particle whose v - t graph is as shown, is back to its starting position.

Two parallel plate capacitors $\text{A}$ and $\text{B}$ have capacitors $1\mu \text{F}$ and $5\mu \text{F}$ are charged separately to same potential of $100\text{V}$. Now the positive plate of $\text{A}$ is connected to the negative plate of $\text{B}$ and the negative plate of $\text{A}$ to the positive plate of $\text{A}$ then the loss of energy in this process is

A wheel performs pure rolling on the ground. Find a point on the periphery of the body which has a velocity equal to the velocity of the centre of mass of the body.

A block of mass $10\text{kg}$ is moving in x-direction with a constant speed of $10\text{m/sec}$. It is subjected to a retarding force $F=-0.1x\text{joule /metre}$ during its travel from $x=20\text{metre}$ to $x=30\text{metre}$. Its final kinetic energy will be

Find the series resonance frequency when L = 0.09 H, C = 25 F

Five identical plates of equal area A are placed parallel to each other with equal distance d between any two adjacent plates, as shown in the figure. The equivalent capacitance of the system between the terminals A and B is



समान क्षेत्रफल A की पाँच एकसमान प्लेटों को एक-दूसरे के समान्तर इस प्रकार रखा जाता है कि किन्हीं दो निकटवर्ती प्लेटों के मध्य समान दूरी चित्रानुसार d हो। टर्मिनलों A व B के मध्य निकाय की तुल्य धारिता है

A rectangular block is heated from $0^{\circ }\text{C}$ to ${100}^{\circ }\text{C}$. The percentage increase in its length is $0.10\%$. What will be the percentage increase in its volume?

A cannon of mass $m_1$ fires a shell of mass $m_2$ with speed $v_0$ relative to the barrel which is inclined at an angle $\alpha$ with horizontal . Find the recoil speed of cannon if it is placed on ice.

The region between two concentric spheres of radii '$a$' and '$b$', respectively (see figure), has volume charge density $\rho =\frac{A}{r}$, where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is

Two particles $A$ and $B$ are moving with equal angular speed $\omega$ as shown in figure. At $t=0$, their positions are shown. Then, relative velocity $\overrightarrow{v_A}-\overrightarrow{v_B}$ at $t=\frac{\pi }{2\omega }$ is

A boat which has a speed $5\text{km/h}$ in still water crosses a river of width $100\text{m}$ along the shortest possible path in $1.5\text{min}$. The velocity of river water in $\text{km/h}$ is

Two identical guitar strings of length $L$ are each tuned exactly to $400\text{Hz}$. The tension in one of the strings is then increased by $2\%$. If they are now struck, what is the beat frequency between the fundamental modes of the two strings?

Assume that a body is displaced from $\overrightarrow{r_A}=(2\text{m},4\text{m},-6\text{m})$ to $\overrightarrow{r_B}=(6\hat{i}-4\hat{j}+2\hat{k})\text{m}$, under a constant force $\overrightarrow{F}=(2\hat{i}+3\hat{j}-\hat{k})\text{N}$. Calculate work done by the force.

A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between the surrounding and each sphere is T, then

For flow through a pipe of radius R, the velocity and temperature distribution are as follows:



$u(r,x)=C_1,andT(r,x)=C_2[1-{\left(\frac{r}{R}\right)}^3]$



where $C_{1}and{C}_2$ are constants.



The bulk temperature is given by



$T_m=\frac{2}{U_m{R}^2}{\int }_0^{R}u(r,x)T(r,x)rdr$ with $U_m$ being the mean velocity of flow. The value of $T_m$ is

Three point charges $q_1=1\mu \text{C},q_2=-2\mu \text{C}$ and $q_3=3\mu \text{C}$ are placed at $(1\text{m},0,0)$ and $(0,2\text{m},0)$ and $(0,0,3\text{m})$ respectively. The electric potential at origin is

The weight of a body will be half its weight on the surface of earth when the distance above the surface of the earth is nearly

The average power dissipated in a pure inductor is

Two strips of metal are riveted together
at their ends by four rivets, each of diameter 6.0 mm. What is the
maximum tension that can be exerted by the riveted strip if the
shearing stress on the rivet is not to exceed 6.9 × 10⁷
Pa? Assume that each rivet is to carry one
quarter of the load.