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A cubical box of volume $216c{m}^3$ is made up of 0.1 cm thick wood. The inside is heated electrically by a 100 W heater. It is found that the temperature difference between the inside and the outside surface is $5^{\circ }C$ in steady state. Assuming that the entire electrical energy spent appears as heat, find the thermal conductivity of the material of the box.

The surface tension of soap solution is $25\times {10}^{-3}N{m}^{-1}$. The excess pressure inside a soap bubble of diameter 1 cm is

What are pseudo forces? Explain using diagrams

A cell of internal resistance $X$ ohms drives current through an external resistance of 6 ohms. The power delivered by the cell to the external resistance will be maximum when

The value of flux due to q through square plate is

The plate current, plate voltage and grid voltage of a 6F6 triode tube are related as
$i_p=41(V_p+7V_g{)}^{1.41}$
Where $V_p$ and $V_g$ are in volts and $i_p$ in microamperes. The tube is operated at $V_p=250V,V_g=-20V.$ Calculate (a) The tube current (b) the plate resistance, (c) the mutual conductance and (d) the amplification factor.

The graph gives the magnitude B(t) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first

Two springs A and B have force constants $k_{1}and{k}_2$ respectively. The ratio of the work done on A to that done on B when they are stretched by the same force is

For a particle moving along $x$ - axis, the acceleration $a$ of the particle in terms of its $x$ - coordinate $x$ is given by $a=-9x$, where $x$ is in meters and $a$ is in ${\text{m/s}}^2$. Take acceleration, velocity and displacement in positive $x$ - direction as positive. The initial velocity of particle at $x=0$ is $u=+6\text{m/s}$. The plot of velocity versus $x$ - coordinate of particle in the duration it moves from origin towards the positive $x$ - direction, is best represented by

A track consists of three semi-circular tracks. Find the ratio of displacement and distance travelled during the motion.

A metal plate is exposed to light of wavelength $\lambda$. It is observed that electrons are ejected from the surface of the plate. When a retarding uniform electric field $E$ is imposed, no electron can move away from the plate farther than a certain distance $d$. Then the threshold wavelength ${\lambda }_0$ for the material of plate is (e is the electronic charge, h is Plank’s constant and $c$ is the speed of light)

A coil has an inductance of $\frac{2.2}{\pi }H$ and is joined in series with a resistance of $220\Omega$. When an alternating emf of 220 V at 50 c.p.s is applied to it, then the wattless component of the rms current in the circuit is ?

A cylinder of mass m and radius r rolls down a circular track from point A as shown in the figure. Assume that the friction is just sufficient to support the rolling. Velocity of the cylinder at point A was zero. Assume r<<R. The reaction by the track on the cylinder at point B is

In the arrangement shown, the acceleration of mass $2m$ is

The equations: $y_1=asin(\omega t–kx)$ and $y_2=–asin(\omega t+kx)$ are for two waves, then the waves will:

The most appropriate curve for magnetization $M$ versus magnetising field $H$ for a paramagnetic substance is

The maximum velocity and acceleration of a particle in $\text{SHM}$ are $100\text{cm/s}$ and $157{\text{cm/s}}^2$ respectively. The time period in seconds will be :

The molar heat capacity in a process of a diatomic gas, if it does a work of $\frac{Q}{4},$ when a heat of $Q$ is supplied to it is

The curve between charge density and distance near P-N junction will be

If $\alpha ,\beta$ be the roots of $a{x}^2+bx+c=0$ and $\gamma ,\delta$ those of $l{x}^2+mx+n=0$, then the equation whose roots are $\alpha \gamma +\beta \delta$ and $\alpha \delta +\beta \gamma$ is

In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is

In the following circuit $i_1$ and $i_2$ are respectively (diodes are ideal)

A body is projected up with a speed $V$ of an inclined plane of angle of inclination β. If the body collides elastically perpendicular to the inclined plane, find the time after which it crosses through its point of projection after collision ?

The surface mass density of a disc of radius $a$ varies with radial distance $r$ as $\sigma =A+Br$ where A & B are positive constants. Then, moment of inertia of the disc about an axis passing through its centre and perpendicular to the plane (in ${\text{kg m}}^2$) is:

A resistor and an inductor are connected to an $\text{AC}$ supply of $120\text{V}$ and $50\text{Hz}$. The current in the circuit is $3\text{A}$. If the power consumed in the circuit is $108W$, then the resistance in the circuit is

On a highway, the maximum speed of vehicles is $25\text{m/s}$. The material of the road provides a coefficient of friction of $0.2$. If the highway has a turn with a radius of curvature of $50\text{m}$, then what should be the banking angle for this turn to ensure the safety of the drivers?

Find the relation between acceleration of $A\left(a\right)$ and acceleration of $B\left(b\right)$ in the figure shown

A motorcycle is going on an over-bridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the over-bridge, the normal force on it

Block $A$ is placed on block $B$, whose mass is greater than that of $A$. There is friction between the blocks, while the ground is smooth. A horizontal force $P$, increasing linearly with time, begins to act on $A$. The accelerations $a_1$ and $a_2$ of $A$ and $B$ respectively are plotted against time ($t$). Choose the correct graph.

A block of mass 10 kg is attached to the end of two light spring balances combination as shown in figure. What mass will each spring reads? (assume springs are collaborated so that its reading provides the mass)

Find the reasing of the spring balance shown in figure. The elevator is going up with an acceleration of g /10, the pulley and the string are light and the pulley is smooth.

A bullet moving with speed $100\text{m/s}$ strikes a block and get embedded into it. If mass of the block is nine times that of the bullet, find the impulse imparted by the bullet to the block (in $\text{Ns}$), given mass of the bullet is $m\text{kg}$.

A ${}^{238}U$ nucleus decays by emitting an alpha particle of speed ${}^{\prime }{v}^{\prime }m{s}^{-1}$. The recoil speed of the residual nucleus (in $m{s}^{-1}$ ) is:

An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57\times {10}^{–2}T$. If the value of $\frac{e}{m}$ is $1.76\times {10}^{11}C/kg$, the frequency of revolution of the electron is

Distinguish between rule and method on the basis of meaning, purpose, source, adherence and penalty.

If a car covers $2/5^{th}$ of the total distance with $v_1$ speed and $3/5^{th}$ distance with $v_2$ speed then, average speed is

A cylinder of radius R is confined to roll without slipping between two planks (above plank moving with velocity v towards right and lower plank with velocity 3v towards right) as shown in the figure. Then

a.) angular velocity of the cylinder is V/R counter clockwise.

b.) angular velocity of the cylinder is 2V/R clockwise

c.) velocity of centre of mass of the cylinder is v towards left

d.) velocity of centre of mass of the cylinder is 2v towards right.

A particle of mass $m$ is attached with four identical springs, each of length $l.$ Initially, each spring has tension $F_0$. Neglecting gravity, calculate the time period for small oscillations of the particle along a line perpendicular to the plane of the figure.

A person is standing in an elevator. In which situation will he find his weight less than his actual weight?

A bob of mass $500\text{g}$ attached to a light inextensible string revolving vertically in a radius $R$ is given an initial velocity $v=\sqrt{7gR}$ at the bottom most point. The tension in the string at the bottom most point is