Question

Column - I gives a list of possible set of parameter measures in some experiments. The variations of the parameters in the form of graphs are shown in Column - II. Match the set of parameters given in Column - I with the graphs given in Column - II.

• A. $A\to p,s;B\to q,s;C\to s;D\to q$
• B. $A\to p,r;B\to q,r;C\to s;D\to q$
• C. $A\to p,r;B\to q,s;C\to r;D\to q$
• D. $A\to p,s;B\to q,s;C\to s;D\to p$

Answer 1

The correct option is A $A\to p,s;B\to q,s;C\to s;D\to q$

$A:$ The graph of potential energy as function of displacement of a simple pendulum will be parabolic graph as given in option $\left(p\right)$. The option $\left(s\right)$ is also correct, if the mean position of the pendulum is at the origin.
Hence $\left(A\right)$ $\to$ $\left(p\right),\left(s\right)$

$B:$ The body is moving along positive x-axis, $v>0$; $y$ is the displacement.
$\therefore y=ut\pm \frac{1}{2}a{t}^2$. For $a=+ve$ and $a=0$, we get graphs which are satisfied by $\left(q\right)$ and $\left(s\right)$.
Hence $\left(B\right)\to \left(q\right),\left(s\right)$

$C:$ $R=\frac{u^{2}sin\left(2\theta \right)}{g}$ and $R\propto u^2$ for a fixed angle of projection and $u=0,R=0$
$\left(C\right)\to \left(s\right)$

$D:$ Time period of a simple pendulum is:
$T=2\pi \sqrt{\frac{l}{g}}$ or $T^2=4{\pi }^2\frac{l}{g}\Rightarrow y=\frac{4{\pi }^2}{g}x$
$\left(D\right)\to \left(q\right)$