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A series combination of n₁ capacitors, each of value C₁, is charged by a source of potential difference 4V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V, it has the same (total) energy stored in it as the first combination has. The value of C₂ in terms of C₁ is:
Force $F$ on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12$ m is:
A particle moves with a velocity $(5\hat i-3\hat j+6\hat k)\text{ ms}^{-1}$ horizontally under the action of a constant force $(10\hat i+10\hat j+20\hat k)\text{ N}$. The instantaneous power supplied to the particle is:
In an experiment four quantities $a$, $b$, $c$ and $d$ are measured with percentage error $1\%$, $2\%$, $3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P = \frac{a^3 b^2}{cd}$. The percentage error in $P$ is
Dimensions of magnetic field intensity is:
A rectangular film of liquid is extended from $(4 \text{ cm} \times 2 \text{ cm})$ to $(5 \text{ cm} \times 4 \text{ cm})$. If the work done is $3 \times 10^{-4} \text{ J}$, then the value of the surface tension of the liquid is:
At what height from the surface of the earth, are the gravitation potential and the value of $g$ are: $-5.4 \times 10^7 \text{ J/kg}$ and $6.0 \text{ ms}^{-2}$ respectively? (Take, the radius of the earth as $6400 \text{ km}$)
The determination of the value of acceleration due to gravity ($g$) by simple pendulum method employs the formula, $g = 4\pi^2 \frac{L}{T^2}$. The expression for the relative error in the value of $g$ is:
The length, breadth, and thickness of a block are given by $l = 12\text{ cm}$, $b = 6\text{ cm}$ and $t = 2.45\text{ cm}$. The volume of the block according to the idea of significant figures should be:
A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. The least count of this vernier calipers is:
If $x = at + bt^2$, where $x$ is the distance travelled by the body in kilometres while $t$ is the time in seconds, then the units of $b$ are
A particle is released from a height $S$ above the surface of the earth. At a certain height, its kinetic energy is three times its potential energy. The height from the earth's surface and the speed of the particle at that instant are respectively:
The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively $4\%$ and $2\%$. The maximum error in the measurement of pressure is
Which relation is wrong?
Which two of the following five physical parameters have the same dimensions? (1) energy density (2) refractive index (3) dielectric constant (4) Young's modulus (5) magnetic field
If a diamagnetic substance is brought near the north or the south pole of a bar magnet, it is
An object is thrown along a direction inclined at an angle of $45^\circ$ with the horizontal direction. The horizontal range of the particle is equal to:
The quantities which have the same dimensions as those of solid angle are:
The earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $R$ from the surface of the earth. The escape velocity of a body from this platform is $fv_e$, where $v_e$ is its escape velocity from the surface of the earth. The value of $f$ is:
A small hole of an area of cross-section $2 \text{ mm}^2$ is present near the bottom of a fully filled open tank of height $2 \text{ m}$. Taking $g = 10 \text{ m/s}^2$, the rate of flow of water through the open hole would be nearly: