Units and Dimensions
Trending Questions
Q. Write the dimensions of (a×b) in the relation E=b−x2at, where E is the energy, x is the displacement and t is time.
- [M−1L2T]
- [M−1L2T−1]
- [ML2T]
- [ML2T−1]
Q. The dimension of the physical quantity x in the equation, F=xρ, where F is force and ρ is density is given by
- [M1L4T−2]
- [M2L−2T−1]
- [M2L−2T−2]
- [M1L−2T−1]
Q. If electronic charge e, electron mass m, speed of light in vaccum c and Plank's constant h are taken as fundamental quantities, the permeability of vaccum μ0 can be expressed in units of
Hint: [h]=[ML2T−1], [μ0]=[MLT−2A−2]
Hint: [h]=[ML2T−1], [μ0]=[MLT−2A−2]
- (hme2)
- (hcme2)
- (hce2)
- (mc2he2)
Q. If C denotes capacitance and V denotes potential difference across the capacitor, the dimensions of CV2 are
- M L T−2
- M2 L T−1
- M L2 T−2
- Not expressible in M L T
Q. If the unit of displacement is micrometer and unit of time is microsecond, the unit of velocity will be
- 10 m/sec
- micrometers
- m/sec
- 100 m/sec
Q. Which of the following is a supplementary physical quantity?
- Mass
- Solid angle
- Energy
- Pressure
Q. Which of the following is derived quantity
- Time
- Mole
- Temperature
- Pressure
Q. The dimension formula of resultant when two quantities of dimensions [MLT−1] are added together, is
- [M0L0T0]
- [MLT−1]
- 2[MLT−1]
- None of these
Q.
A metal with work function of 3.7 eV is being used in a photoelectric experiment. A light source is switched on and light is allowed to fall on the plate such that it delivers 10 eV to each electron. Find the kinetic energy with which the electrons will come out?
6.3 eV
7.3 eV
(0 - 6.3 ) eV
None of these
Q. Which of the following is a supplementary physical quantity?
- Mass
- Solid angle
- Energy
- Pressure
Q. A physical quantity X is expressed as velocity =√(Xdensity). The dimensions of X are
- [ML2T−2]
- [ML−1T−2]
- [ML2T−1]
- [MLT−1]
Q. The dimensional formula for relative density is
- [ML−3]
- [M0L−3]
- [M0L0T−1]
- [M0L0T0]
Q. Hertz is the unit for
- Frequency
- Velocity
- Force
- Electric charge
Q. In order to measure physical quantities in the sub-atomic world, the quantum theory often employs energy E, angular momentum J and velocity c as fundamental dimensions instead of the usual mass, length and time. Then, the dimension of force in this theory is
- [E]2[J][c]
- [E]2[J]2[c]
- [E][J][c]
- [E][J][c]
Q. Which of the following is usually a derived quantity?
- Velocity
- Length
- Mass
- Time
Q. Suppose the kinetic energy of a body oscillating with amplitude A and at a distance x is given by K=Bxx2+A2. The dimensions of B are the same as that of
- work / time
- work × distance
- work / distance
- work × time
Q. The dimension formula of resultant when two quantities of dimensions [MLT−1] are added together, is
- [M0L0T0]
- [MLT−1]
- 2[MLT−1]
- None of these
Q. Hertz is the unit for
- Frequency
- Force
- Electric charge
- Velocity
Q. A light-year is a unit of
- time
- mass
- distance
- energy
Q. The period of a body under SHM is represented by T=PaDbSc, where P is pressure, D is density and S is surface tension. The value of a, b and c are
- a=−32, b=12, c=1
- a=12, b=12, c=1
- a=2, b=1, c=1
- a=1, b=1, c=1
Q. Which of the following is not the name of a physical quantity?
- meter
- impulse
- energy
- density
Q. Dimensional formula M L−1 T−2 doesnot represent the physical quantity
- Pressure
- Young's modulus of elasticity
- Stress
- Strain
Q. If u1 and u2 are the units selected in two systems of measurement and n1 and n2 are their numerical values respectively, then for constant physical quantity
- n1u1=n2u2
- n1u1+n2u2=0
- n1n2=u1u2
- n1+u1=n2+u2
Q. If electronic charge e, electron mass m, speed of light in vaccum c and Plank's constant h are taken as fundamental quantities, the permeability of vaccum μ0 can be expressed in units of
Hint: [h]=[ML2T−1], [μ0]=[MLT−2A−2]
Hint: [h]=[ML2T−1], [μ0]=[MLT−2A−2]
- (hme2)
- (hcme2)
- (hce2)
- (mc2he2)
Q. If electronic charge e, electron mass m, speed of light in vaccum c and Plank's constant h are taken as fundamental quantities, the permeability of vaccum μ0 can be expressed in units of
Hint: [h]=[ML2T−1], [μ0]=[MLT−2A−2]
Hint: [h]=[ML2T−1], [μ0]=[MLT−2A−2]
- (hme2)
- (hcme2)
- (hce2)
- (mc2he2)
Q. In a new system of units, the fundamental quantities mass, length and time are replaced by acceleration a, density ρ and frequency f. The dimensional formula for force in this system is
- [ρa3f−6]
- [ρa4f−6]
- [ρa4f6]
- [ρ−1a4f−6]
Q. The CGS system was the first system to be developed as a standardized set of units.
- True
- False
Q. The dimensions of the quantities in one (or more) of the following pairs are the same. Identify the pair(s).
(Given, Torque=Force×distance,
Angular momentum=momentum×distance
Young's modulus=stressstrain, Stress=ForceArea, Strain=Change in lengthOriginal length
(Given, Torque=Force×distance,
Angular momentum=momentum×distance
Young's modulus=stressstrain, Stress=ForceArea, Strain=Change in lengthOriginal length
- Torque and work
- Angular momentum and work
- Energy and Young’s modulus
- Light year and wavelength
Q. A boy recalls the relation almost correctly but forgets where to put the constant c i.e. speed of light. He writes m=m0√1−v2, where m and m0 stand for masses and v for speed. Right place of c is
- m=cm0√1−v2
- m=m0c√1−v2
- m=m0√c2−v2
- m=m0√1−v2c2
Q. Which of the following is not a fundamental physical quantity?
- Temperature
- Mass
- Length
- Density