CBSE Class 11 Physical World and Measurement Worksheet A

Question. The magnitude of any physical quantity:
a. Depends on the method of measurement
b. Does not depend on the method of measurement
c. Is more in SI system than in CGS system
d. Directly proportional to the fundamental units of mass, length and time
Answer : B

Question. One nanometre is equal to:
a. 109 mm
b. 10^–6 mm
c. 10^–7 cm
d. 10^–9 mm
Answer : C

Question. Which is different from others by units?
a. Phase difference
b. Mechanical equivalent
c. Loudness of sound
d. Poisson's ratio
Answer : D

Question. If velocity v , acceleration A and force F are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of v, A and F would be
a. FA⁻¹ v
b. Fv³ A⁻¹
c. Fv² A⁻¹
d. F² v² A⁻¹
Answer : B

Question. Density of wood is 0.5 gm/cc in the CGS system of units.
The corresponding value in MKS units is:
a. 500
b. 5
c. 0.5
d. 5000
Answer : A

Question. Young's modulus of a material has the same units as:
a. Pressure
b. Strain
c. Compressibility
d. Force
Answer : A

Question. Select the pair whose dimensions are same:
a. Pressure and stress
b. Stress and strain
c. Pressure and force
d. Power and force
Answer : A

Question. If x = at + bt² , where x is the distance travelled by the body in kilometres while t is the time in seconds, then the units of b are:
a. km / s
b. km – s
c. km / s²
d. km – s²
Answer : C

Question. The unit of absolute permittivity is:
a. Farad - meter
b. Farad / meter
c. Farad / meter ²
d. Farad
Answer : B

Question. Given that v is speed, r is the radius and g is the acceleration due to gravity. Which of the following is dimensionless?
a. v² / rg
b. v² r / g
c. v² g / r
d. v² rg
Answer : A

Question. The dimension of the ratio of angular to linear momentum is:
a. M⁰ L¹ T⁰
b. M¹ L¹ T⁻¹
c. M¹ L² T⁻¹
d. M⁻¹ L⁻¹ T⁻¹
Answer : A

Question. In S = a +bt +ct² . S is measured in metres and t in seconds. The unit of c is:
a. ms^–2
b. m
c. ms^–1
d. None of these
Answer : A

Question. If the time period (T) of vibration of a liquid drop depends on surface tension (S), radius (r) of the drop and density (ρ)of the liquid, then the expression of T is:

Answer : A

Question. The equation of a wave is given by A Y = sin ω (x/v - k) where ω is the angular velocity and v is the linear velocity. The dimension of k is:
a. LT
b. T
c. T⁻¹
d. T²
Answer : B

Question. Unit of Stefan's constant is:
a. Js^–1
b. Jm^–2 s⁻¹ K^–4
c. Jm^–2
d. Js
Answer : B

Question. The unit of surface tension in SI system is:
a. 2 Dyne / cm
b. Newton/m
c. Dyne/cm
d. Newton/m²
Answer : B

Question. The SI unit of universal gas constant (R) is:
a. Watt K⁻¹ mol⁻¹
b. Newton K⁻¹ mol⁻¹
c. Joule K⁻¹ mol⁻¹
d. Erg K⁻¹ mol⁻¹
Answer : C

Question. The equation of the stationary wave is y = 2a sin(2πct/λ) cos (2πx/λ) which of the following statements is wrong:
a. The unit of ct is same as that of λ
b. The unit of x is same as that of λ
c. The unit of 2πc /λ is same as that of 2πx /λt
d. The unit of c/λ is same as that of x /λ
Answer : D

Question. The temperature of a body on Kelvin scale is found to be X K. When it is measured by a Fahrenheit thermometer, it is found to be X F. Then X is:
a. 301.25
b. 574.25
c. 313
d. 40
Answer : C

Question. X = 3YZ² find dimension of Y in (MKSA) system, if X and Z are the dimension of capacity and magnetic field respectively:
a. M L T A⁻³
b. ML⁻²
c. M⁻³ L⁻² T⁴ A⁴
d. M⁻³ L⁻² T⁸ A⁴
Answer : D

Question. E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of El² / m² G² are:
a. Angle
b. Length
c. Mass
d. Time
Answer : A

Question. The dimensions of coefficient of thermal conductivity is:
a. ML⁻² T² K⁻¹
b.MLT⁻³ K⁻¹
c. MLT⁻² K⁻¹
d. MLT⁻³ K
Answer : B

Question. The velocity of water waves v may depend upon their wavelength λ , the density of water ρ and the acceleration due to gravity g . The method of dimensions gives the relation between these quantities as:
a. v² ∝ λ g ⁻¹ ρ⁻¹
b. v² ∝ gλρ
c. v² ∝ gλ
d. v² ∝ g⁻¹ λ⁻³
Answer : C

Question. A physical quantity is measured and its value is found to be nu where n = numerical value and u = unit. Then which of the following relations is true:
a. 2 n ∝ u
b. n ∝ u
c. n ∝ √u
d. n ∝ 1/u
Answer : D

Question. In C.G.S. system the magnitude of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, metre and minute, the magnitude of the force is:
a. 0.036
b. 0.36
c. 3.6
d. 36
Answer : C

Question. If velocity v, acceleration A and force F are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of v, A and F would be:
a. FA⁻¹ v
b. Fv³ A⁻²
c. Fv² A⁻¹
d. F² v² A⁻¹
Answer : B

Question. The largest mass (m) that can be moved by a flowing river depends on velocity (v), density (ρ), of river water and acceleration due to gravity (g). The correct relation is:

Answer : D

Question. A physical quantity is given by X = M^a L^b T^c . The percentage error in measurement of M, Land T are α ,β and γ respectively. Then maximum percentage error in the quantity X is:
a. aα + bβ + cγ
b. aα + bβ − cγ
c. a/α + b/β + c/γ
d. None of these
Answer : A

Question. From the dimensional consideration, which of the following equation is correct?

Answer : A

Question. A highly rigid cubical block A of small mass M and side L is fixed rigidly onto another cubical block B of the same dimensions and of low modulus of rigidity η such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn block A executes small oscillations. The time period of which is given by:

Answer : D

Question. A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a = b^α c^β / d^γ e^δ If the maximum errors in the measurement of b, c, d and e are b₁ %, c₁ %, d₁ % and e₁ %, then the maximum error in the value of a determined by the experiment is:
a. (b₁ + c₁ + d₁ + e₁ )%
b. (b₁ + c₁ − d₁ −e₁ )%
c. (αb₁ + βc₁ − γd₁ − δe₁ )%
d. (αb₁ +βc₁ +γd₁ +δe₁ )%
Answer : D

Question. The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is:
a. 1%
b. 2%
c. 6%
d. 8%
Answer : D

Question. The relative density of material of a body is found by weighing it first in air and then in water. If the weight in air is (5.00 ±0.05 ) Newton and weight in water is (4.00 ±0.05) Newton. Then the relative density along with the maximum permissible percentage error is:
a. 5.0 ±11%
b. 5.0 ±1%
c. 5.0 ±6%
d. 1.25 ±5%
Answer : A

1. If x = at + bt² where x is in meters and t is in seconds. What are the units of a and b?

2. Fill ups.

(i) 3.0m/s² = --------------------- km/hr²

(ii) 6.67 10^-11Nm²/kg² = ------------------------- g^-1cm³s^-2]

3. Write S.I unit of luminous intensity and temperature? 

4. Calculate the time taken by the light to pass through a nucleus of diameter 1.56x 10^-16 m. (speed of light is 3x 10⁸ m/s)

5. If force (F) acceleration (A) and time (T) are taken as fundamental units, then find the dimension of energy.

6. Two resistances R1 = 100 ±3Ω and R₂ = 200 ±4Ω are connected in series. Then what is the equivalent resistance?

7. If velocity, time and force were chosen the basic quantities, find the dimensions of mass?

8. Young’s modulus of steel is 19x10¹⁰ N/m². Express it in dynes cm². Here dynes are the C.G.S unit of force.

9. The velocity u of water waves may depend on their wavelengthl density of water r and the acceleration due to gravity g. Find relation between these quantities by the method of dimension?

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