Advertisements
Advertisements
प्रश्न
A new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. How much will 5 J measure in this new system?
उत्तर
For solving this problem, dimensions of physical quantity will remain the same whatever the system of units of its measurement.
Let the physical quantity be Q = n1u1 = n2u2
Let M1, L1, T1 and M2, L2, T2 be units of mass, length and time in the given two systems.
So, `n_2 = n_1 [M_1/M_2]^a xx [L_1/L_2]^b xx [T_1/T_2]^c`
We know that dimension of energy `[U] = [ML^2T^-2]`
According to the problem, M1 = 1 kg, L1 = 1 m, T1 = 1 s
M2 = α kg, L2 = β m, T2 = γ s
Substituting the values, we get
`n_2 = 5 [M_1/M_2] xx [L_1/L_2]^2 xx [T_1/T_2]^-2`
= `5[1/α kg] xx [1/β m]^2 xx [1/γ s]^-2`
= `5 xx 1/α xx 1/β^2 xx 1/γ^-2`
= `(5γ^2)/(αβ^2) J`
This is the required value of energy in the new system of units.
APPEARS IN
संबंधित प्रश्न
Explain this statement clearly:
“To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary:
- Atoms are very small objects
- A jet plane moves with great speed
- The mass of Jupiter is very large
- The air inside this room contains a large number of molecules
- A proton is much more massive than an electron
- The speed of sound is much smaller than the speed of light.
A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance?
A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ m0 of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes:
`m = m_0/(1-v^2)^(1/2)`
Guess where to put the missing c.
Fill in the blank by suitable conversion of unit:
3.0 m s–2= ______ km h–2
Fill in the blank by suitable conversion of unit:
G= 6.67 × 10–11 N m2 (kg)–2= ______ (cm)3s–2 g–1
In which of the following systems can scientific data be exchanged between different parts of the world?
Young’s modulus of steel is 1.9 × 1011 N/m2. When expressed in CGS units of dynes/cm2, it will be equal to (1N = 105 dyne, 1m2 = 104 cm2)
Photon is quantum of radiation with energy E = h ν where ν 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
During a total solar eclipse the moon almost entirely covers the sphere of the sun. Write the relation between the distances and sizes of the sun and moon.
Calculate the solid angle subtended by the periphery of an area of 1 cm2 at a point situated symmetrically at a distance of 5 cm from the area.
