On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct?
$y = a \sin 2 \pi t / T$
$y = a \sin vt$
$y = \frac {a} {T} \sin \left( \frac {t} {a} \right)$
$y = a \sqrt{2} \left( \sin \frac{2\pi t}{T} - \cos \frac{2\pi t}{T} \right)$
If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
(P - Q)/R
PQ - R
PQ/R
(PR - Q2)/R
(R + Q)/P
Photon is quantum of radiation with energy E = hv, where v is frequency and h is Planck’s constant. The dimensions of h are the same as that of
linear impulse
angular impulse
linear momentum
angular momentum
If Planck’s constant ($h$) and speed of light in vacuum ($c$) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass and time in terms of the three chosen fundamental quantities?
Mass of electron ($m_e$)
Universal gravitational constant ($G$)
Charge of electron ($e$)
Mass of proton ($m_p$)
Which of the following ratios express pressure?
Force/Area
Energy/Volume
Energy/Area
Force/Volume