\(A, B, C\) and \(D\) are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation \(AD = C\, ln\, (BD)\) holds true. Then which of the combination is not a meaningful quantity ?

In the electric network shown, when no current flows through the \(4\, \Omega \) resistor in the arm \(EB\), the potential difference between the points \(A\) and \(D\) will be ............... \(V\)

The radius of \(R\) of a nucleus of mass number \(A\) can be estimated by the formula \(R =\left(1.3 \times 10^{-15}\right) A ^{1 / 3}\, m .\) It follows that the mass density of a nucleus is of the order of \(\left( M _{\text {prot. }} \cong M _{\text {neut. }}=1.67 \times 10^{-27} kg \right)\)

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is \(10\,s^{-1}\).  At, \(t = 0\) the displacement is \(5\, m\). What is the maximum acceleration ? The initial phase is \(\frac{\pi }{4}\)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .
Assertion A : If oxygen ion \(\left(\mathrm{O}^{-2}\right)\) and Hydrogen ion \(\left(\mathrm{H}^{+}\right)\)enter normal to the magnetic field with equal momentum, then the path of \(\mathrm{O}^{-2}\) ion has a smaller curvature than that of \(\mathrm{H}^{+}\).
Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.
In the light of the above statements, choose the correct answer from the options given below :

A vertical electric field of magnitude \(4.9 \times 10^{5} N / C\) just prevents a water droplet of a mass \(0.1\, g\) from falling. The value of charge on the droplet will be  ........ \(\times 10^{-9} \;C\) \(\left(\right.\) Given \(\left.g =9.8 m / s ^{2}\right)\)

Moment of inertia of a square plate of side \(l\) about the axis passing through one of the corner and perpendicular to the plane of square plate is given by

As shown in the figure, a bob of mass \(\mathrm{m}\) is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius \(\mathrm{r}\) and mass \(m\). When released from rest the bob starts falling vertically. When it has covered a distance of \(h\). the angular speed of the wheel will be

A batsman hits back a ball of mass \(0.4 \; kg\) straight in the direction of the bowler without changing its initial speed of \(15 \; ms ^{-1}\). The impulse imparted to the ball is \(\dots \; Ns\)