TS EAMCET · Physics · Units and Dimensions
If L and C are inductance and capacitance respectively, then the dimensional formula of \((\mathrm{LC})^{-\frac{1}{2}}\) is
- A \(\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-1}\right]\)
- B \(\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-1}\right]\)
- C \(\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^1\right]\)
- D \(\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-2}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-1}\right]\)
Step-by-step Solution
Detailed explanation
\([L] = [ML^2T^{-2}A^{-2}]\) \([C] = [M^{-1}L^{-2}T^4A^2]\) \([LC] = [ML^2T^{-2}A^{-2}][M^{-1}L^{-2}T^4A^2] = [T^2]\) \([ (LC)^{-\frac{1}{2}} ] = ([T^2])^{-\frac{1}{2}} = [T^{-1}]\) \([ (LC)^{-\frac{1}{2}} ] = [M^0 L^0 T^{-1}]\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A TV transmitting antenna is \(128 \mathrm{~m}\), tall. If the receiving antenna is at the ground level, the maximum distance between, them for satisfactory communication in line of sight mode is (radius of the earth \(6.4 \times 10^6 \mathrm{~m}\) )TS EAMCET 2014 Easy
- The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius \(r\) to an orbit of radius \(\frac{3 r}{2}\) isTS EAMCET 2023 Hard
- A conducting wire is in the shape of a regular hexagon which is inscribed inside an imaginary circle of radius \(R\). If a current \(I\) flows the wire, the magnitude of magnetic field at the centre of the circle is
TS EAMCET 2020 Medium - Two cells \(A\) and. \(B\) are connected in the secondary circuit of a potentiometer one at a time and the balancing length are respectively \(400 \mathrm{~cm}\) and \(440 \mathrm{~cm}\). The emf of the cell \(A\) is 1.08 volt. The emf of the second cell \(B\) in volts isTS EAMCET 2004 Medium
- The mean free path for a gas at temperature and pressure torr is The mean free path of the gas at a temperature and pressure torr will beTS EAMCET 2021 Easy
- Two particles of equal mass have velocities \(\overrightarrow{\mathbf{v}}_1=4 \hat{\mathbf{i}}\) and \(\overrightarrow{\mathbf{v}}_2=4 \hat{\mathbf{j}} \mathrm{ms}^{-1}\). First particle has an acceleration \(\overrightarrow{\mathbf{a}}_1=(5 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}) \mathrm{ms}^{-2}\) while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path ofTS EAMCET 2004 Easy
More PYQs from TS EAMCET
- What is the binding energy of whose atomic mass is Mass of proton Mass of neutron (Neglect the electron mass) (Assume )TS EAMCET 2020 Easy
- In a junction transistor, the collector current changes by \(6.8 \mathrm{~mA}\), if the emitter current is changed by \(7 \mathrm{~mA}\). For such transistor, the current amplification factor isTS EAMCET 2018 Medium
- A block is in simple harmonic motion (S.H.M) on the end of the spring with position given by \(x=(5) \cos \left(\omega t+\frac{\pi}{4}\right)\) If the total mechanical energy used is 100 J to achieve maximum displacement, then the potential energy at time t = 0 isTS EAMCET 2022 Medium
- According to the photoelectric effect, the plot of kinetic energy of the emitted photo-electrons from a metal versus the frequency of the incident radiation gives a straight line whose slopeTS EAMCET 2020 Easy
- A block of mass 2 kg is tied to one end of a. 2 m long metal wire of \(1.0 \mathrm{~mm}^2\) area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is 2 mm , the Young's modulus of the metal is (Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )TS EAMCET 2024 Hard
- Three long, straight, parallel wires carrying different currents are arranged as shown in the diagram. In the given arrangement, let the net force per unit length on the wire ' \(C\) ' be \(\vec{F}\). If the wire ' \(B\) ' is removed without disturbing the other two wires, then the force per unit length on wire ' \(\mathrm{A}\) ' is
TS EAMCET 2023 Medium