List of top Questions asked in MHT CET

A sonometer wire gives frequency \( f_1 \) with tension \( T_1 \). If the tension is made 4 times greater, what is the new frequency? The frequency of a vibrating wire is related to the tension in the wire by the equation: \[ f \propto \sqrt{T} \] where:
\( f \) is the frequency,
\( T \) is the tension in the wire.

If the tension is increased by a factor of 4, how does the frequency change?

In a parallel bridge circuit involving capacitors, the circuit's resultant capacitance is to be determined. If the capacitance values are given, calculate the resultant capacitance in the parallel combination. Assume the capacitors have the following capacitance values:
\( C_1 = 2 \, \mu\text{F} \) 
\( C_2 = 3 \, \mu\text{F} \)
\( C_3 = 4 \, \mu\text{F} \)

The capacitors are connected in parallel.

A magnetic field is produced along the axis of a current-carrying loop. The direction and magnitude of the magnetic field at the center of the loop can be determined using the Biot-Savart law. What will be the direction of the magnetic field along the axis of the current loop? The magnetic field produced along the axis of a circular current loop is given by the equation: \[ B = \frac{{\mu_0 I R^2}}{{2 (R^2 + x^2)^{3/2}}} \]
where:
\( B \) is the magnetic field,
\( \mu_0 \) is the permeability of free space,
\( I \) is the current,
\( R \) is the radius of the loop,
\( x \) is the distance from the center of the loop along the axis.

A beam of unpolarized light is incident on a polarizer. The intensity of the transmitted light is measured as it passes through the polarizer. If the angle between the light's initial direction and the axis of the polarizer is \( \theta \), what is the intensity of the transmitted light? The intensity of the transmitted light is given by Malus' law: \[ I = I_0 \cos^2 \theta \]
where:
\( I_0 \) is the intensity of the unpolarized light before passing through the polarizer,
\( \theta \) is the angle between the light's initial direction and the axis of the polarizer.

In a photoelectric effect experiment, light of wavelength \( \lambda \), \( \lambda/2 \), and \( \lambda/6 \) are incident on a metal surface. The stopping potential for these wavelengths are given as \( V_1 \), \( V_2 \), and \( V_3 \), respectively. If the work function of the metal is \( \phi \), calculate the work function using the given wavelengths. The photoelectric equation is given by: \[ E_k = h \nu - \phi \] where:
\( E_k \) is the kinetic energy of the emitted electrons (which is related to the stopping potential),
\( h \) is Planck's constant,
\( \nu \) is the frequency of the incident light,
\( \phi \) is the work function of the metal.

The frequency \( \nu \) is related to the wavelength \( \lambda \) by the equation: \[ \nu = \frac{c}{\lambda} \] where \( c \) is the speed of light.

A body is floating in oil. The density of the oil is \( \rho_{\text{oil}} \) and the density of the body is \( \rho_{\text{body}} \). If the body is partially submerged, what is the fraction of the body's volume submerged in the oil?
Given:
\( \rho_{\text{oil}} \) = density of the oil,
\( \rho_{\text{body}} \) = density of the body.