The \(x-t\) graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at \(t=\frac{4}{3} \mathrm{~s}\) is

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When liquid medicine of density \(\rho\) is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop.
We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension \(T\) when the radius of the drop is \(R\). When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.Question :
After the drop detaches, its surface energy is

Consider a body of mass $1.0 kg$ at rest at the origin at time $t=0$. A force $\overrightarrow{F}=\left(\alpha t\widehat{i}+\beta \widehat{j}\right)$ is applied on the body, where $\alpha =1.0N{s}^{-1}and \beta =1.0N$ . The torque acting on the body about the origin at time $=1.0 s \mathrm{i}\mathrm{s} \overrightarrow{\tau }$ . Which of the following statements is (are) true?

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular
magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. \(I_1\) and \(I_2\) are the currents in the segments \(a b\) and \(c d\). Then,

A circular disc of radius $R$ carries surface charge density $\sigma \left(r\right)={\sigma }_0\left(1-\frac{r}{R}\right)$, where ${\sigma }_0$ is a constant and $r$ is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is ${\varphi }_0$. Electric flux through another spherical surface of radius $\frac{R}{4}$ and concentric with the disc is $\varphi$. Then the ratio $\frac{{\varphi }_0}{\varphi }$ is

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is

Two co-axial conducting cylinders of same length \(\ell\) with radii \(\sqrt{2} R\) and \(2 R\) are kept, as shown in Fig. 1. The charge on the inner cylinder is \(Q\) and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant \(\kappa=5\). Consider an imaginary plane of the same length \(\ell\) at a distance R from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross-sectional view of this arrangement is shown in Fig. 2. Ignoring edge effects, the flux of the electric field through the plane is ( \(\epsilon_0\) is the permittivity of free space):

Match the integrals in Column I with the values in Column II.

To form a complete monolayer of acetic acid on \(1 \mathrm{~g}\) of charcoal, \(100 \mathrm{~mL}\) of \(0.5 \mathrm{M}\) acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 \(\mathrm{mL}\) of \(1 \mathrm{M} \mathrm{NaOH}\) solution was required. If each molecule of acetic acid occupies \(\mathbf{P} \times 10^{-23} \mathrm{~m}^2\) surface area on charcoal, the value of \(\mathbf{P}\) is _______ [Use given data: Surface area of charcoal \(=1.5 \times 10^2 \mathrm{~m}^2 \mathrm{~g}^{-1} ;\) Avogadro's number \(\left(\mathrm{N}_{\mathrm{A}}\right)=6.0 \times 10^{23}\) \(\left.\mathrm{mol}^{-1}\right]\)

Statement I Molecules that are not superimposable on their mirror images are chiral.
Statement II All chiral molecules have chiral centres.

A solid sphere is in pure rolling motion on an inclined surface having inclination \(\theta\).

Let $X$ be the set of all five digit numbers formed using $1,2,2,2,4,4,0$. For example, $22240$ is in $X$ while $02244$ and $44422$ are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that an element chosen at random is a multiple of $20$ given that it is a multiple of $5$. Then the value of $38 p$ is equal to

The correct statement(s) about the compound given below is are