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The total radiant energy per unit area per unit time, normal to the direction of incidence, received at a distance $R$ from the centre of a star of radius $r$, whose outer surface radiates as a black body at a temperature $T\text{ K}$ is given by (where $\sigma$ is Stefan's constant):
When $1\text{ kg}$ of ice at $0^{\circ}\text{C}$ melts to water at $0^{\circ}\text{C}$, the resulting change in its entropy, taking latent heat of ice to be $80\text{ cal/g}$, is
A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance $r$. The speed of the particle is:
An engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is reduced by $62^{\circ}\text{C}$, its efficiency is doubled. The temperature of the source is:
A refrigerator works between $4^{\circ}\text{C}$ and $30^{\circ}\text{C}$. It is required to remove $600 \text{ calories}$ of heat every second to keep the temperature of the refrigerated space constant. The power required will be: (Take, $1 \text{ cal} = 4.2 \text{ Joules}$)
If the force on a rocket having an exhaust velocity of $300 \text{ m/s}$ is $210 \text{ N}$, then the rate of combustion of the fuel is:
The value of coefficient of volume expansion of glycerin is $5 \times 10^{-4}\text{ K}^{-1}$. The fractional change in the density of glycerin for a rise of $40^{\circ}\text{C}$ in its temperature is -
Light with an energy flux of $25 \times 10^4$ Wm$^{-2}$ falls on a perfectly reflecting surface at normal incidence. If the surface area is 15 cm$^2$, then the average force exerted on the surface is:
The energy of the EM wave is of the order of $15 \text{ keV}$. To which part of the spectrum does it belong?
Two bodies of equal masses revolve in circular orbits of radii R₁ and R₂ with the same period. Their centripetal forces are in the ratio:
A truck and a car are moving with equal velocity. If equal retarding force is applied on each, then on applying the brakes both will stop after certain distance:
Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 10.0 Ω is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. The value of X is:
A coil of resistance $400\Omega$ is placed in a magnetic field. If the magnetic flux $\phi\;(\text{Wb})$ linked with the coil varies with time $t\;(\text{sec})$ as $\phi=50t^2+4$. The current in the coil at $t=2\text{s}$ is:
A coin, placed on a rotating turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is tripled, it will just slip, if its distance from the centre is:
When $1 \text{ kg}$ of ice at $0^{\circ}\text{C}$ melts into water at $0^{\circ}\text{C}$, the resulting change in its entropy, taking the latent heat of ice to be $80 \text{ cal/g}$, is:
When a string is divided into three segments of lengths $l_1, l_2$ and $l_3$, the fundamental frequencies of these three segments are $\nu_1, \nu_2$ and $\nu_3$ respectively. The original fundamental frequency ($\nu$) of the string is:
Given below are two statements: Assertion (A): A standing bus suddenly accelerates. If there was no friction between the feet of a passenger and the floor of the bus, the passenger would move back. Reason (R): In the absence of friction, the floor of the bus would slip forward under the feet of the passenger.
A wooden stick of length $3l$ is rotated about an end with constant angular velocity $\omega$ in a uniform magnetic field $B$ perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is:
The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi = \phi_0 + 4t$, where $\phi$ is in Weber, $t$ is time in seconds, and $\phi_0$ is a constant, the output voltage across the secondary coil is:
The variation of electrostatic potential with radial distance $r$ from the centre of a positively charged metallic thin shell of radius $R$ is given by the graph: