Download App

STD 11 - 13. oscillations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 13. oscillations4 Marks
MCQ
A simple pendulum of length $1\,m$ is allowed to oscillate with amplitude $2^o$. It collides elastically with a wall inclined at $1^o$ to the vertical. Its time period will be : (use $g = \pi ^2$ )
  • A
    $2/3\,sec$
  • ✓
    $4/3\,sec$
  • C
    $2\,sec$
  • D
    None of these
✓

Answer

Correct option: B.
$4/3\,sec$
b
Time period for half part $T=2 \pi \sqrt{\frac{1}{g}}=2 \pi \sqrt{\frac{1}{g}}=2 \pi \sqrt{\frac{1}{g}}=\frac{2 \pi}{g}=2 \mathrm{sec}$

So $2^{\circ}$ part will be covered in a time $t=\frac{T}{2}=1$ sec

For the half $1^{\circ}$ part

$\theta=\theta_{2} \sin (\omega t)$

$1^{\circ}=2^{\circ} \sin \left(\frac{2 \pi}{T} \times t\right) \Rightarrow \frac{t}{2}=\sin \left(\frac{2 \pi}{T} \times t\right)$

$\Rightarrow \frac{\pi}{6}=\pi \times 1 \Rightarrow t=1 / 6 \mathrm{sec}$

Total time $\Rightarrow \frac{T}{2}+2 t$

$\Rightarrow 1+2 \times \frac{1}{6}=1+\frac{1}{3}=\frac{4}{3} \mathrm{sec}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Four metallic plates arearranged as shown in the figure. If the distance between each plate then capacitance of the given system between points $A$ and $B$ is (Given $d < < A$)
→
A resistance of $4\,\Omega $ and a wire of length $5\,m$ and resistance $5\,\Omega $ are joined in series and connected to a cell of $e.m.f.$ $10\, V$ and internal resistance $1\,\Omega $. A parallel combination of two identical cells is balanced across $300\, cm$ of the wire. The $e.m.f.$ $E$ of each cell is ........... $V$
→
A body of mass $m$ is at rest. Another body of same mass moving with velocity $ V $ makes head on elastic collision with the first body. After collision the first body starts to move with velocity
→
A planet is revolving ground the sun in an elliptical orbit. Its closest distance from the sun is $r_{min}$ , the farthest distance from the sun is  $r_{max}$ . If the orbital angular velocity of the planet when it is the nearest to the sun is $\omega $, then the orbital angular velocity at the point when it is at the farthest distance from the sun is
→
The error in measuring the current with a tangent galvanometer is minimum when the deflection is about.....$^o$
→
Select the correct statement about the reflection and refraction of a wave at the interface between the medium $1$ and $2$ the
→
The temperature at which root mean square speed of a gas will be half of its value at $0\,^oC$ is ....... $^oC$
→
A bubble of $8$ mm diameter is formed in the air. The surface tension of soap solution is $30$ dynes/cm. The excess pressure inside the bubble is ........ $dynes/cm^2$
→
A monochromatic light is incident from air on a refracting surface of a prism of angle $75^{\circ}$ and refractive index $n_0=\sqrt{3}$. The other refracting surface of a prism is coated by a thin film of material of refractive index $n$ as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $\theta \leq 60^{\circ}$. The value of $n ^2$ is. . . . . 
→
A tunnel is dug across the diameter of earth $A$ ball is released from the surface of  Earth into the tunnel. The velocity of ball when it is at a distance $\frac{R}{2}$ from  centre of earth is (where $R$ = radius of Earth and $M$ = mass of Earth)
→