Question Bank Directory

In a guitar, two strings $A$ and $B$ made of same material are slightly out of tune and produce beats of frequency $6 \text{ Hz}$. When tension in $B$ is slightly decreased, the beat frequency increases to $7 \text{ Hz}$. If the frequency of $A$ is $530 \text{ Hz}$, the original frequency of $B$ will be:

A spherical body of mass m and radius r is allowed to fall in a medium of viscosity η. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant (τ). Dimensionally τ can be represented by:

Which of the following pairs of physical quantities has the same dimensions?

If $P$ represents radiation pressure, $c$ represents speed of light and $Q$ represents radiation energy striking a unit area per second, then non-zero integers $x, y$ and $z$ such that $P^x Q^y c^z$ is dimensionless, are

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: $P=\frac{a^3b^2}{cd}$. Percentage error in $P$ is:

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:

Length cannot be measured by

The method used to remove temporary hardness of water is :

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?

The correct order of increasing electron gain enthalpy with a negative sign for the elements O, S, F, and Cl is:

In a region, the potential is represented by $V(x, y, z) = 6x - 8xy - 8y + 6yz$, where $V$ is in volts and $x, y, z$ are in meters. The electric force experienced by a charge of $2$ coulomb situated at a point $(1, 1, 1)$ is:

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 temperature inside a refrigerator is $t_2^\circ\text{C}$ and the room temperature is $t_1^\circ\text{C}$. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be: