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The period of a body under SHM is presented by $T = P^a D^b S^c$; where $P$ is pressure, $D$ is density and $S$ is surface tension. The value of $a$, $b$ and $c$ are:
If potential in a region is expressed as $V(x,y,z) = 6xy - y + 2yz$, the electric field at point $(1, 1, 0)$ is:
The dimensions of universal gravitational constant are
Of the following quantities, which one has dimensions different from the remaining three?
A, B and C are three points in a uniform electric field. The electric potential is:
If energy ($E$), velocity ($v$) and time ($T$) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:
The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f = C m^x K^y; where C is a dimensionless quantity. The value of x and y are:
Three capacitors each of capacitance $C$ and of breakdown voltage $V$ are joined in series. The capacitance and breakdown voltage of the combination will be:
Two spheres of radius $a$ and $b$ respectively are charged and joined by a wire. The ratio of the electric field at the surface of the spheres is:
Out of the following, the only pair that does not have identical dimensions is
The unit of thermal conductivity is:
The electric potential at a point in free space due to a charge $Q$ coulomb is $Q \times 10^{11}$ V. The electric field at that point is:
Joule-second is the unit of:
A screw gauge has the least count of $0.01\text{ mm}$ and there are $50$ divisions in its circular scale. The pitch of the screw gauge is:
The velocity $v$ of a particle at time $t$ is given by $v = at + \frac{b}{t+c}$, where $a$, $b$ and $c$ are constants. The dimensions of $a$, $b$ and $c$ are respectively:
The angle of $1'$ (minute of an arc) in radian is nearly equal to:
Two metal spheres, one of radius $R$ and the other of radius $2R$ respectively have the same surface charge density $\sigma$. They are brought in contact and separated. What will be the new surface charge densities on them?
A Screw Gauge gives the following readings when used to measure the diameter of a wire. Main scale reading = $0.0\text{ mm}$ Circular scale reading = $52\text{ divisions}$ Given that: $1\text{ mm}$ on the main scale corresponds to $100\text{ divisions}$ of the circular scale. The diameter of the wire from the above data is:
Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$, length $L$, time $T$, and current $I$, would be:
Which one has the dimensions different from the remaining three?