JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
If the velocity of light \(c\), universal gravitational constant \(G\) and planck's constant \(h\) are chosen as fundamental quantities. The dimensions of mass in the new system is
- A \(\left[h^{\frac{1}{2}} c^{-\frac{1}{2}} G^1\right]\)
- B \(\left[ h ^1 c ^1 G ^{-1}\right]\)
- C \(\left[ h ^{-\frac{1}{2}} c ^{\frac{1}{2}} G ^{\frac{1}{2}}\right]\)
- D \(\left[h^{\frac{1}{2}} c^{\frac{1}{2}} G ^{-\frac{1}{2}}\right]\)
Answer & Solution
Correct Answer
(D) \(\left[h^{\frac{1}{2}} c^{\frac{1}{2}} G ^{-\frac{1}{2}}\right]\)
Step-by-step Solution
Detailed explanation
Say dimensional formale of mass is \(H ^{ x } C ^{ y } G ^z\) \(M ^1=\left( ML ^2 T ^{-1}\right)^{ x }\left( LT ^{-1}\right)\left( M ^{-1} L ^3 T ^{-2}\right)^Z\) \(M ^1 L ^0 T ^0= M ^{ x - z } L ^{2 x + y +3 z} T ^{- x - y -2 z}\) on comparing both side \(x-z=1\)…
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
- In a double slit experiment, at a certain point on the screen the path difference between the two interfering waves is \(\frac{1}{8} ^{th}\) of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe isJEE Mains 2020 Medium
- Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : The photoelectric effect does not take place, if the energy of the incident radiation is less than the work function of a metal. Reason \(R\) : Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal. In the light of the above statements, choose the most appropriate answer from the options given belowJEE Mains 2022 Medium
- \(M\) grams of steam at \(100^{\circ} \mathrm{C}\) is mixed with \(200\; \mathrm{g}\) of ice at its melting point in a thermally insulated container. If it produces liquid water at \(40^{\circ} \mathrm{C}\) [heat of vaporization of water is \(540 \;cal/\mathrm{g}\) and heat of fusion of ice is \(80 \;\text { cal/g }]\) the value of \(\mathrm{M}\) isJEE Mains 2020 Medium
- Red light differs from blue light as they have :JEE Mains 2021 Medium
- A slanted object \(A B\) is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is:
JEE Mains 2025 Medium - The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: \((i)\) a ring of radius \(R,\,(ii)\) a solid cylinder of radius \(\frac {R}{2}\) nd \((iii)\) a solid sphere of radius \(\frac {R}{4}.\) If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb isJEE Mains 2019 Hard
More PYQs from JEE Mains
- If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are \(a, b\) and \(c\) respectively, then the corresponding ratio of increase in their lengths is
JEE Mains 2013 Hard - The coefficient of static friction between a wooden block of mass \(0.5\, kg\) and a vertical rough wall is \(0.2\) The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be \(N\) \(\left[ g =10\, ms ^{-2}\right]\)JEE Mains 2021 Medium
- If \((1 - x^3)^{10} = \sum\limits_{r=0}^{10} a_r x^r (1-x)^{30-2r}\), then \(\dfrac{9a_9}{a_{10}}\) is equal to __________.JEE Mains 2026 Hard
- If for \(n \geq 1\) , \({P_n} = \int\limits_1^e {{{\left( {\log \,x} \right)}^n}\,dx} \) , then \(P_{10} - 90P_8\) is equal toJEE Mains 2014 Hard
- The \(X-Y\) plane be taken as the boundary between two transparent media \(M _{1}\) and \(M _{2} . M _{1}\) in \(Z \geq 0\) has a refractive index of \(\sqrt{2}\) and \(M _{2}\) with \(Z <0\) has a refractive index of \(\sqrt{3}\). A ray of light travelling in \(M_{1}\) along the direction given by the vector \(\overrightarrow{ A }=4 \sqrt{3 i }-3 \sqrt{3 \hat{j}}-5 \hat{ k }\), is incident on the plane of separation. The value of difference between the angle of incident in \(M _{1}\) and the angle of refraction in \(M _{2}\) will be \(....\) degree.JEE Mains 2022 Hard
- The velocity-time graphs of a car and a scooter are shown in the figure. \((i)\) the difference between the distance travelled by the car and the scooter in \(15\, s\) and \((ii)\) the time at which the car will catch up with the scooter are, respectively
JEE Mains 2018 Hard