# Units and Measurement Test 5

Total Questions:50 Total Time: 60 Min

Remaining:

## Questions 1 of 50

Question:Which of the following is not a unit of energy

$$W{\rm{ - s}}$$

$$kg{\rm{ - }}m/\sec$$

$$N{\rm{ - }}m$$

Joule

## Questions 2 of 50

Question:In $$S = a + bt + c{t^2}$$. $$S$$ is measured in metres and $$t$$ in seconds. The unit of $$c$$ is

None

$$m$$

$$m{s^{ - 1}}$$

$$m{s^{ - 2}}$$

## Questions 3 of 50

Question:Joule-second is the unit of

Work

Momentum

Pressure

Angular momentum

## Questions 4 of 50

Question:The unit of surface tension in SI system is

$$Dyne/c{m^2}$$

$$Newton/m$$

$$Dyne/cm$$

$$Newton/{m^2}$$

## Questions 5 of 50

Question:The unit of reduction factor of tangent galvanometer is

Ampere

Gauss

None of these

## Questions 6 of 50

Question:The unit of self inductance of a coil is

Henry

Weber

Tesla

## Questions 7 of 50

Question:$$Ampere - hour$$ is a unit of

Quantity of electricity

Strength of electric current

Power

Energy

## Questions 8 of 50

Question:The unit of specific resistance is

$$Ohm/c{m^2}$$

$$Ohm/cm$$

$$Ohm - cm$$

$${(Ohm - cm)^{ - 1}}$$

## Questions 9 of 50

Question:The binding energy of a nucleon in a nucleus is of the order of a few

$$eV$$

$$Ergs$$

$$MeV$$

$$Volts$$

## Questions 10 of 50

Question:In SI, Henry is the unit of

Self inductance

Mutual inductance

(1) and (2) both

None of the above

## Questions 11 of 50

Question:The unit of $$e.m.f.$$is

Joule

Joule-Coulomb

Voltâ€“Coulomb

Joule/Coulomb

## Questions 12 of 50

Question:Which of the following is not the unit of time

Micro second

Leap year

Lunar months

Parallactic second

Solar day

## Questions 13 of 50

Question:Which is not a unit of electric field

$$N{C^{ - 1}}$$

$$V{m^{ - 1}}$$

$$J{C^{ - 1}}$$

$$J{C^{ - 1}}{m^{ - 1}}$$

## Questions 14 of 50

Question:The correct value of $${0^o}C$$ on the Kelvin scale is

$$273.15K$$

$$272.85\,K$$

$$273\,K$$

$$273.2\,K$$

## Questions 15 of 50

Question:'Torr' is the unit of

Pressure

Volume

Density

Flux

Charge

emf

Mass

Energy

## Questions 17 of 50

Question:Candela is the unit of

Electric intensity

Luminous intensity

Sound intensity

None of these

## Questions 18 of 50

Question:The unit of reactance is

Ohm

Volt

Mho

Newton

## Questions 19 of 50

Question:Dimensional formula $$M{L^2}{T^{ - 3}}$$ represents

Force

Power

Energy

Work

## Questions 20 of 50

Question:The dimensions of calorie are

$$M{L^2}{T^{ - 2}}$$

$$ML{T^{ - 2}}$$

$$M{L^2}{T^{ - 1}}$$

$$M{L^2}{T^{ - 3}}$$

## Questions 21 of 50

Question:Whose dimensions is $$M{L^2}{T^{ - 1}}$$

Torque

Angular momentum

Power

Work

## Questions 22 of 50

Question:The dimensional formula for $$r.m.s.$$ (root mean square) velocity is

$${M^0}L{T^{ - 1}}$$

$${M^0}{L^0}{T^{ - 2}}$$

$${M^0}{L^0}{T^{ - 1}}$$

$$ML{T^{ - 3}}$$

## Questions 23 of 50

Question:The dimensional formula for Planck's constant $$(h)$$ is

$$M{L^{ - 2}}{T^{ - 3}}$$

$$M{L^2}{T^{ - 2}}$$

$$M{L^2}{T^{ - 1}}$$

$$M{L^{ - 2}}{T^{ - 2}}$$

## Questions 24 of 50

Question:Out of the following, the only pair that does not have identical dimensions is

Angular momentum and Planck's constant

Moment of inertia and moment of a force

Work and torque

Impulse and momentum

## Questions 25 of 50

Question:The equation of a wave is given by $$Y = A\sin \omega \left( {\frac{x}{v} - k} \right)$$ where $$\omega$$ is the angular velocity and $$v$$ is the linear velocity. The dimension of $$k$$ is

$$LT$$

$$T$$

$${T^{ - 1}}$$

$${T^2}$$

## Questions 26 of 50

Question:The dimensions of coefficient of thermal conductivity is

$$M{L^2}{T^{ - 2}}{K^{ - 1}}$$

$$ML{T^{ - 3}}{K^{ - 1}}$$

$$ML{T^{ - 2}}{K^{ - 1}}$$

$$ML{T^{ - 3}}K$$

## Questions 27 of 50

Question:Which one has the dimensions different from the remaining three

Power

Work

Torque

Energy

## Questions 28 of 50

Question:A small steel ball of radius $$r$$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $$\eta$$. After some time the velocity of the ball attains a constant value known as terminal velocity $${v_T}$$. The terminal velocity depends on (i) the mass of the ball $$m$$, (ii) $$\eta$$, (iii) $$r$$ and (iv) acceleration due to gravity $$g$$. Which of the following relations is dimensionally correct

$${v_T} \propto \frac{{mg}}{{\eta r}}$$

$${v_T} \propto \frac{{\eta r}}{{mg}}$$

$${v_T} \propto \eta rmg$$

$${v_T} \propto \frac{{mgr}}{\eta }$$

## Questions 29 of 50

Question:The quantity $$X = \frac{{{\varepsilon _0}LV}}{t}$$: $${\varepsilon _0}$$ is the permittivity of free space, $$L$$is length, $$V$$ is potential difference and $$t$$ is time. The dimensions of $$X$$ are same as that of

Resistance

Charge

Voltage

Current

## Questions 30 of 50

Question:If $$P$$ represents radiation pressure, $$c$$ represents speed of light and $$Q$$ represents radiation energy striking a unit area per second, then non-zero integers $$x,\,y$$ and $$z$$ such that $${P^x}{Q^y}{c^z}$$ is dimensionless, are

$$x = 1,\,\,y = 1,\,\,z = - 1$$

$$x = 1,\,y = - 1,\,z = 1$$

$$x = - 1,\,y = 1,\,z = 1$$

$$x = 1,\,y = 1,\,z = 1$$

## Questions 31 of 50

Question:Inductance $$L$$ can be dimensionally represented as

$$M{L^2}{T^{ - 2}}{A^{ - 2}}$$

$$M{L^2}{T^{ - 4}}{A^{ - 3}}$$

$$M{L^{ - 2}}{T^{ - 2}}{A^{ - 2}}$$

$$M{L^2}{T^4}{A^3}$$

## Questions 32 of 50

Question:Dimensions of strain are

$$ML{T^{ - 1}}$$

$$M{L^2}{T^{ - 1}}$$

$$ML{T^{ - 2}}$$

$${M^0}{L^0}{T^0}$$

## Questions 33 of 50

Question:The dimensions of Planck's constant and angular momentum are respectively

$$M{L^2}{T^{ - 1}}$$ and $$ML{T^{ - 1}}$$

$$M{L^2}{T^{ - 1}}$$ and $$M{L^2}{T^{ - 1}}$$

$$ML{T^{ - 1}}$$ and $$M{L^2}{T^{ - 1}}$$

$$ML{T^{ - 1}}$$ and $$M{L^2}{T^{ - 2}}$$

## Questions 34 of 50

Question:Let $$[{\varepsilon _0}]$$ denotes the dimensional formula of the permittivity of the vacuum and $$[{\mu _0}]$$ that of the permeability of the vacuum. If $$M = {\rm{mass}}$$, $$L = {\rm{length}}$$, $$T = {\rm{Time}}$$ and $$I = {\rm{electric current}}$$, then

$$[{\varepsilon _0}] = {M^{ - 1}}{L^{ - 3}}{T^2}I$$

$$[{\varepsilon _0}] = {M^{ - 1}}{L^{ - 3}}{T^4}{I^2}$$

$$[{\mu _0}] = ML{T^{ + 2}}{I^{ + 2}}$$

$$[{\mu _0}] = M{L^2}{T^{ - 1}}I$$

## Questions 35 of 50

Question:Dimensions of $$CR$$ are those of

Frequency

Energy

Time period

Current

## Questions 36 of 50

Question:Dimension of electric current is

$$[{M^0}{L^0}{T^{ - 1}}Q]$$

$$[M{L^2}{T^{ - 1}}Q]$$

$$[{M^2}L{T^{ - 1}}Q]$$

$$[{M^2}{L^2}{T^{ - 1}}Q]$$

## Questions 37 of 50

Question:The fundamental physical quantities that have same dimensions in the dimensional formulae of torque and angular momentum are

Mass, time

Time, length

Mass, length

Time, mole

## Questions 38 of 50

Question:If pressure $$P$$, velocity $$V$$ and time $$T$$ are taken as fundamental physical quantities, the dimensional formula of force is

$$P{V^2}{T^2}$$

$${P^{ - 1}}{V^2}{T^{ - 2}}$$

$$PV{T^2}$$

$${P^{ - 1}}V{T^2}$$

## Questions 39 of 50

Question:Identify the pair whose dimensions are equal

Torque and work

Stress and energy

Force and stress

Force and work

## Questions 40 of 50

Question:The dimensions of pressure is equal to

Force per unit volume

Energy per unit volume

Force

Energy

## Questions 41 of 50

Question:Which of the two have same dimensions

Force and strain

Force and stress

Angular velocity and frequency

Energy and strain

## Questions 42 of 50

Question:The dimensions of shear modulus are

$$ML{T^{ - 1}}$$

$$M{L^2}{T^{ - 2}}$$

$$M{L^{ - 1}}{T^{ - 2}}$$

$$ML{T^{ - 2}}$$

## Questions 43 of 50

Question:Pressure gradient has the same dimension as that of

None of these

## Questions 44 of 50

Question:If force (F), length (L) and time (T) are assumed to be fundamental units, then the dimensional formula of the mass will be

$$F{L^{ - 1}}{T^2}$$

$$F{L^{ - 1}}{T^{ - 2}}$$

$$F{L^{ - 1}}{T^{ - 1}}$$

$$F{L^2}{T^2}$$

## Questions 45 of 50

Question:What is the number of significant figures in 0.310 Ã— 10$$^3$$

2

3

4

6

## Questions 46 of 50

Question:Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is

1%

3%

5%

7%

## Questions 47 of 50

Question:The mean time period of second's pendulum is 2.00s and mean absolute error in the time period is 0.05s. To express maximum estimate of error, the time period should be written as

(2.00 $$\pm$$ 0.01) s

(2.00 +0.025) s

(2.00 $$\pm$$ 0.05) s

(2.00 $$\pm$$ 0.10) s

## Questions 48 of 50

Question:In an experiment, the following observation's were recorded : L = 2.820 m, M = 3.00 kg, l = 0.087 cm, Diameter D = 0.041 cm Taking g = 9.81 $$m/{s^2}$$using the formula , Y=$$\frac{{4MgL}}{{\pi {D^2}l}}$$, the maximum permissible error in Y is

7.96%

4.56%

6.50%

8.42%

## Questions 49 of 50

Question:According to Joule's law of heating, heat produced $$H = {I^2}$$ Rt, where I is current, R is resistance and t is time. If the errors in the measurement of I, R and t are 3%, 4% and 6% respectively then error in the measurement of H is

$$\pm$$17%

$$\pm$$16%

$$\pm$$19%

$$\pm$$25%

## Questions 50 of 50

Question:If there is a positive error of 50% in the measurement of velocity of a body, then the error in the measurement of kinetic energy is