NEET Practice Questions (MCQs) with Answers & Solutions

When a simple pendulum is suspended from the roof of a vehicle moving down an inclined plane without friction, the effective acceleration due to gravity experienced by the pendulum is g cos(θ), where θ is the angle of inclination. Therefore, the time period is T = 2π√(L/(g cos(θ))), where L is the length of the pendulum.

b)  The wire may be treated as a string for which force constant                                                         $k_1=\frac{Force}{Extencion }=\frac{YA}{L}\left(Y=\frac{F}{A}\times \frac{L}{∆L}\right)$

   Spring constant of the spring $k_2=K$

Hence spring constant of the combination (series)

$k_{eq}=\frac{k_1{k}_2}{k_1-k_2}=\left(\frac{(YA/L)K}{\left(YA/L\right)+K }\right)=\frac{YAK}{YA+KL}$

$⊝$Time period $T=2\pi \sqrt{\frac{m}{k}}=2\mathrm{\pi }{\left[\frac{\left(\mathrm{YA}+ \mathrm{KL}\right)\mathrm{m}}{\mathrm{YAK}}\right]}^{1/2}$

(b) For forced oscillation,

       $x=x_0 \sin \left(\omega t+\varnothing \right)and F=F_0 \cos \omega t$

    where, $x_0=\frac{F}{m\left({{\omega }^2}_0-{\omega }^2\right)} \propto \frac{1}{m\left({{\omega }^2}_0-{\omega }^2\right)}$

(b)

 $$\begin{gathered} y=4 {\cos }^2\left(\frac{t}{2}\right)\sin 1000t \\ \Rightarrow y=2\left(1+\cos t\right) \sin \left(1000t\right) \left(As 1+\cos t=1+2{\cos }^2\left(\frac{t}{2}\right)-1=2{\cos }^2\left(\frac{t}{2}\right)\right) \\ \Rightarrow y=2 \sin 1000t+2 \sin 1000t \cos t \\ \Rightarrow y=2 \sin 1000t+\sin \left(1000t-t\right)+\sin (1000t+t) \left[2\sin A\cos B=\sin \left(A+B\right)+\sin \left(A-B\right)\right] \\ \Rightarrow y= 2 \sin 1000t + \sin 999t+ \sin 1001t \\ \mathrm{It} \mathrm{is} \mathrm{a} \mathrm{sum} \mathrm{of} \mathrm{three} \mathrm{S}.\mathrm{H}.\mathrm{M}. \end{gathered}$$

$$\begin{gathered} \mathrm{y} = \mathrm{a} \sin \left(\mathrm{\omega t} - \mathrm{kx}\right) \\ \mathrm{speed} \mathrm{of} \mathrm{wave} = \frac{\mathrm{\omega }}{\mathrm{k}} \\ = \frac{314}{3.14} = 100 \mathrm{m}/\mathrm{s} \end{gathered}$$

$y=A \log x +B\log x is not a wave.$

2$\pi$

$$\begin{gathered} \mathrm{v} = \sqrt{\frac{{\mathrm{E}}_{}}{\mathrm{\rho }}}\left\{\mathrm{Laplace} \mathrm{formula}\right\} \\ \mathrm{v} \propto \sqrt{{\mathrm{E}}_{\mathrm{a}}} \end{gathered}$$

When a wave undergoes a reflection at a denser medium then it's crest reflected as a trough and vice versa.

When a source of sound moves away from a stationary observer, the frequency heard by the observer decreases due to the Doppler effect. The observed frequency is given by f' = f * (v - v_s) / (v + v_s), where f is the source frequency, v is the speed of sound, and v_s is the speed of the source. As the source moves away with the speed of sound, the observed frequency is halved.