List of practice Questions

During SHM, K.E. of particle in SHM varies with frequency of 176 Hz. Find the frequency of SHM of the particle.

Detector \( D \) moves from \( A \) to \( B \) and observes the frequencies are differing by 10 Hz. The source is emitting frequency \( f_0 \) as shown: Speed of detector is 35 times less than speed of sound. Then \( f_0 \) is.

Two mechanical waves on strings of equal length (\( L \)) and tension (\( T \)) having linear mass density \( \mu_1/\mu_2 = 1/2 \). Find the ratio of time taken for a wave pulse to travel from one end to the other in both strings. (Ignore gravity)

A simple pendulum of length $30$ cm makes $20$ oscillations in $10$ s on a certain planet. Another pendulum makes $40$ oscillations in $10$ s on the same planet. Find the length of the second pendulum.

Statement–I: Time period of a simple pendulum increases if the mass of the bob is increased.
Statement–II: Time period of a simple pendulum depends only on its length and acceleration due to gravity.

A particle moves according to the equation x = Asin(\(\omega t\)). The potential energy is maximum at time \(t = \frac{T}{2\beta}\), where T is the time period of particle. Find the minimum value of \(\beta\) :

System is released after slightly stretching it. Find angular frequency of its oscillations:

A curve is given between the potential energy \(U\) of a particle and its position on the \(x\)-axis as shown. Given: \[ \tan\theta_1 = 1,\qquad \tan\theta_2 = 3,\qquad \tan\theta_3 = -\frac{1}{2} \] If \(F_{AB}\) is the force acting on the particle during motion from \(A\) to \(B\), similarly \(F_{BC}\), \(F_{CD}\) and \(F_{DE}\) are the forces during \(B\) to \(C\), \(C\) to \(D\) and \(D\) to \(E\) respectively, arrange the magnitudes of these forces in decreasing order.

Position \( x \) of the particle of mass 2 kg varies as function of time as \( x = t^2 + t + 1 \). Find out work done on the particle from \( t_1 = 2 \) sec to \( t_2 = 3 \) sec.

A curve is given between potential energy of a particle and its position on the x-axis.

Given: \( \tan \theta_1 = 1, \, \tan \theta_2 = 3, \, \tan \theta_3 = -\frac{1}{2} \)
If \( F_{AB} \) be the force acting on the particle during \( A \) to \( B \), similarly \( F_{BC}, F_{CD}, \, F_{DE} \) are the forces during \( B \) to \( C \), \( C \) to \( D \), and \( D \) to \( E \) respectively. Arrange magnitudes of these forces in decreasing order.

A ball of mass 100 g is projected with velocity 20 m/s at $60^\circ$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is:

A body of mass 4 kg is placed on a plane at a point P having coordinate $(3,4)$ m. Under the action of force $\vec{F} = (2\hat{i} + 3\hat{j})$ N, it moves to a new point Q having coordinates $(6,10)$ m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of:

$\text{C}_3\text{H}_6\text{Cl}_2$ (X) $\xrightarrow[\Delta]{\text{NaNH}_2 (2 \text{eq})}$ (Y) $\xrightarrow[\text{(ii) NaBH}_4]{\text{(i) Hg(OAc)}_2/\text{H}_2\text{O}}$ $\text{CH}_3\text{COCH}_3$. (Y) $\xrightarrow[\Delta]{\text{Fe/tube}}$ (Z).
Statement-I : Y gives yellow ppt. with $\text{NaOH}/\text{I}_2$.
Statement-II : Two types of H-atoms and one aromatic ring is present in Z and ratio of Z and X is 1 : 3.
Choose the correct option.

In the given situation, the force at the center on 1 kg mass is \( F_1 \). Now if \( 4m \) and \( 3m \) are interchanged, the force is \( F_2 \). Given \( \frac{F_1}{F_2} = \frac{2}{\sqrt{\alpha}} \), find \( \alpha \).

Time taken to achieve terminal velocity by a body depends on density of material (\(\rho\)), density of liquid (\(\sigma\)), radius of material (r) and viscosity of liquid (\(\eta\)) as \(t = k\rho^a r^b \eta^c \sigma^d\). Find \(\frac{b+c}{a+d}\) ?

If \(6\int_{1}^{x} f(t)dt = 3x f(x) + x^3 - 4, x \geq 1\) then value of (f(2)-f(3)) is :

Ratio of de-Broglie wavelengths of a proton and an alpha particle accelerated through the same potential is:

Detector $D$ moves from $A$ to $B$ and observes that the frequencies differ by $10\ \text{Hz}$. The source is emitting frequency $f_0$ as shown. The speed of the detector is $35$ times less than the speed of sound. Then $f_0$ is:

Two coherent loudspeakers \(L_1\) and \(L_2\) are placed at a separation of \(10\,\text{m}\) parallel to a wall at a distance of \(40\,\text{m}\) as shown in the figure. On a width \(AB\) on the wall, 10 maxima and minima are found. If the velocity of sound is \(324\,\text{m s}^{-1}\), find the frequency of sound. (Given: \( \sqrt{5}=2.23 \)).

Speed of sound at \(T_1 = 0^\circ C\) is \(V_0\) and at \(T_2 = \alpha^\circ C\) speed becomes \(2V_0\). Find \(\alpha\):