Download App

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

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 13. oscillations4 Marks
MCQ
The $x$-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=4 / 3 \mathrm{~s}$ is
  • A
    $\frac{\sqrt{3}}{32} \pi^2 \mathrm{~cm} / \mathrm{s}^2$
  • B
    $\frac{-\pi^2}{32} \mathrm{~cm} / \mathrm{s}^2$
  • C
    $\frac{\pi^2}{32} \mathrm{~cm} / \mathrm{s}^2$
  • ✓
    $-\frac{\sqrt{3}}{32} \pi^2 \mathrm{~cm} / \mathrm{s}^2$
✓

Answer

Correct option: D.
$-\frac{\sqrt{3}}{32} \pi^2 \mathrm{~cm} / \mathrm{s}^2$
d
The correct option is $D -\frac{\sqrt{3} \pi^2}{32} cm / s ^2$ From the $x-t$ graph of the particle,

At, $t =0$, the particle is at $x =0$.

Hence, the particle is starting $SHM$ from its mean position.

The equation of $SHM$ of particle will be, $x=A \sin \omega t$ $\qquad$

From the graph, one oscillation has been completed in time, $T =8 s$ and maximum displacement, $A=1 cm$

So, angular frequency, $\omega=\frac{2 \pi}{T}=\frac{2 \pi}{8}=\frac{\pi}{4} rad / s$

On putting above data in $(1)$

$x=1 \sin \left(\frac{\pi t}{4}\right)$

At, $t=\frac{4}{3} s$

$x=1 \sin \left(\frac{\pi}{4} \times \frac{4}{3}\right)=\frac{\sqrt{3}}{2} cm$

Now,

Acceleration of the particle at $t=\frac{4}{3} s$,

$a=-\omega^2 x=-\left(\frac{\pi}{4}\right)^2 \times \frac{\sqrt{3}}{2}$

$\Rightarrow a=-\frac{\sqrt{3} \pi^2}{32} cm / s ^2$

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

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

Similar questions

The figure shows the $P-V$ plot of an ideal gas taken through a cycle $ABCDA.$ The part $ABC$ is a semicircle and $CDA$ is half of an ellipse. Then,
→
When a ceiling fan is switched off, its angular velocity falls to half while it makes $36$ $rotations.$ How many more rotations will it make before coming to rest (Assume uniform angular retardation)
→
The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are the Young's modulus of the materials, then
→
A satellite of the earth is revolving in circular orbit with a uniform velocity $V.$ If the gravitational force suddenly disappears, the satellite will
→
Two satellites $\mathrm{P}$ and $\mathrm{Q}$ are moving in different circular orbits around the Earth (radius $R$ ). The heights of $\mathrm{P}$ and $\mathrm{Q}$ from the Earth surface are $h_{\mathrm{p}}$ and $h_{\mathrm{Q}}$, respectively, where $h_{\mathrm{p}}=\mathrm{R} / 3$. The accelerations of $\mathrm{P}$ and $\mathrm{Q}$ due to Earth's gravity are $g_{\mathrm{p}}$ and $g_{\mathrm{Q}}$, respectively. If $g_{\mathrm{p}} / g_{\mathrm{Q}}=36 / 25$, what is the value of $h_Q$ ?
→
If body having initial velocity zero is moving with uniform acceleration $8\,\,m/{\sec ^2}$ the distance travelled by it in fifth second will be.........$metres$
→
An astronomical refracting telescope is being used by an observer to observe planets in normal adjustment. The focal lengths of the objective and eye piece used in the construction of the telescope are $20\,m$ and $2\,cm$ respectively. Consider the following statements about the telescope :

$(a)$ The distance between the objective and eye piece is $20.02\; m$

$(b)$ The magnification of the telescope is $1000$

$(c)$ The image of the planet is erect and diminished

$(d)$ The aperture of eye piece is smaller than that of objective

The correct statements are :

→
$V-i$ graphs for parallel and series combination of two identical resistors are as shown in figure. Which graph represents parallel combination
→
Four charge $Q _1, Q _2, Q _3$, and $Q _4$, of same magnitude are fixed along the $x$ axis at $x =-2 a - a ,+ a$ and $+2 a$, respectively. A positive charge $q$ is placed on the positive $y$ axis at a distance $b > 0$. Four options of the signs of these charges are given in List-$I$ . The direction of the forces on the charge q is given in List-$II$ Match List-$1$ with List-$II$ and select the correct answer using the code given below the lists.$Image$
List-$I$ List-$II$
$P.$ $\quad Q _1, Q _2, Q _3, Q _4$, all positive $1.\quad$ $+ x$
$Q.$ $\quad Q_1, Q_2$ positive $Q_3, Q_4$ negative $2.\quad$ $-x$
$R.$ $\quad Q_1, Q_4$ positive $Q_2, Q_3$ negative $3.\quad$ $+ y$
$S.$ $\quad Q_1, Q_3$ positive $Q_2, Q_4$ negative $4.\quad$ $-y$

→
Match List-$I$ with List-$II$ :

List-$I$ List-$II$
$(A)$  A force thatrestores anelastic body of unit area to its original state $(I)$ Bulkmodulus
$(B)$  Two equal andopposite forcesparallel toopposite faces $(II)$Young'smodulus
$(C)$Forcesperpendiculareverywhere tothe surface perunit areasameeverywhere $(III)$ Stress
$(D)$Two equal andopposite forceperpendicular toopposite faces $(IV)$ Shearmodulus

Choose the correct answer from the options given below:

→