A simple perdulum performs simple harmonic motion about x=0 with … - Vidyadip

MCQ

A simple perdulum performs simple harmonic motion about $x=0$ with an amplitude $a$ and time period $T$. The speed of the pendulum at $x=a/2$ will be

A
$\frac{{\pi A}}{T}$
B
$\;\frac{{3{\pi ^2}A}}{T}$
✓
$\;\frac{{\pi A\sqrt 3 }}{T}$
D
$\;\frac{{\pi A\sqrt 3 }}{{2T}}$

✓

Answer

Correct option: C.

$\;\frac{{\pi A\sqrt 3 }}{T}$

c
For simple harmonic motion,

$v=\omega \sqrt{a^{2}-x^{2}}$

When $x=\frac{a}{2}, v=\omega \sqrt{a^{2}-\frac{a^{2}}{4}}=\omega \sqrt{\frac{3}{4} a^{2}}$

As $\omega=\frac{2 \pi}{T}, \quad \therefore \quad v=\frac{2 \pi}{T} \cdot \frac{\sqrt{3}}{2} a \Rightarrow \quad v=\frac{\pi \sqrt{3} a}{T}$

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

More "M.C.Q (1 Marks)" from 13. oscillations→13. oscillations — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Disc $A$ and disc $B$ with a hole have equal mass and radius and a string is wrapped around them as shown. Equal force $F$ is applied on the string of each body. Friction is sufficient for rolling. After time $t$ velocity of $A$ is $v_A$ and that of $B$ is $v_B$ and kinetic energy $k_A$ & $k_B$ , then

The standing wave in a medium is expressed as $y=0.2 \sin (0.8 x) \cos (3000 t) \,m$. The distance between any two consecutive points of minimum or maximum displacement is

If earth suddenly stop rotating, then the weight of an object of mass $m$ at equator will $[\omega$ is angular speed of earth and $R$ is its radius]

The dimension of $\frac{1}{2} \varepsilon_0 E ^2$, where $\varepsilon_0$ is permittivity of free space and $E$ is electric field, is

Three particles $A, B$ and $C$ each of mass $m$ are lying at the corners of an equilateral triangle of side $L$. If the particle $A$ is released keeping the particles $B$ and $C$ fixed, the magnitude of instantaneous acceleration of $A$ is ........

The mass density of a planet of radius $R$ varies with the distance $r$ from its centre as $\rho( r )=\rho_{0}\left(1-\frac{ r ^{2}}{ R ^{2}}\right) .$ Then the gravitational field is maximum at

A particle executes $SHM $ in a line $4\, cm $ long. Its velocity when passing through the centre of line is $12\, cm/s$. The period will be ..... $s$

Angle between the vectors $(\hat i + \hat j)$ and $(\hat j - \hat k)$ is ........ $^o$

If the length of the second's hand in a stop clock is $3 \,cm$ the angular velocity and linear velocity of the tip is

A particle is projected with speed $u$ at angle $\theta$ with horizontal from ground. If it is at same height from ground at time $t_1$ and $t_2$, then its average velocity in time interval $t_1$ to $t_2$ is .........