MCQ
In the relation $y = a\cos (\omega t - kx)$, the dimensional formula for $k$ is
- A$[{M^0}{L^{ - 1}}{T^{ - 1}}]$
- B$[{M^0}L{T^{ - 1}}]$
- ✓$[{M^0}{L^{ - 1}}{T^0}]$
- D$[{M^0}LT]$
✓
Answer
Correct option: C.
$[{M^0}{L^{ - 1}}{T^0}]$
c
(c) $[Kx]$ = Dimension of $\omega t = $(dimensionless)
(c) $[Kx]$ = Dimension of $\omega t = $(dimensionless)
hence $K = \frac{1}{X} = \frac{1}{L} = \left[ {{L^{ - 1}}} \right]$
$⇒$ $[K] = [{L^{ - 1}}]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are
→For a system to be in equilibrium, the torques acting on it must balance. This is true only if the torques are taken about
Two stones are thrown with same speed $u$ at different angles from ground in air. If both stones have same range and height attained by them are $h_1$ and $h_2$, then $h_1+h_2$ is equal to .......
→Diagrams show readings of a screw gauge. figure $(i)$ shows the zero error reading when the screw gauge is closed, figure $(ii)$ the reading when the screw gauge is being used to measure the diameter of a ball-bearing. What is the diameter of the ball-bearing in $mm$? There are $50$ divisions on circular scale
→At $100 \,K$ and $0.1$ atmospheric pressure, the volume of helium gas is $10 \,litres.$ If volume and pressure are doubled, its temperature will change to ....... $K$
→Five particles have speeds $1, 2, 3, 4, 5 \,\,m/s$. the average velocity of the particles is (in $m/s$)
→In steel, the Young's modulus and the strain at the breaking point are $2 \times 10^{11}\ Nm^{-2}$ and $0.15,$ respectively. The stress at the breaking point for steel is therefore:
→Water is flowing on a horizontal fixed surface, such that its flow velocity varies with $y$ (vertical direction) as $v=k\left(\frac{2 y^2}{a^2}-\frac{y^3}{a^3}\right)$. If coefficient of viscosity for water is $\eta$, what will be shear stress between layers of water at $y=a$.
→$Y = A \sin \left(\omega t +\phi_{0}\right)$ is the time-displacement equation of a SHM. At $t=0$ the displacement of the particle is $Y =\frac{ A }{2}$ and it is moving along negative $x$ -direction. Then the initial phase angle $\phi_{0}$ will be ...... .
→Four mole of hydrogen, two mole of helium and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture?