MCQ | Units and Dimensions

PRACTICE TEST – I

Question :1  [ML^-1T^-2] is the dimensional formula of

(A) force

(B) coefficient of friction

(C) modulus of elasticity

(D) energy

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Ans: (C)

 

Question :2 The dimensional formula of coefficient of viscosity is

(A) [MLT^-1]

(B) [M^-1L²T^-2]

(C) [ML^-1T ^-1]

(D) none of these

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Ans: (C)

 

Question :3 On the basis of dimensional equation, the maximum number of unknown that can be found, is

(A) one

(B) two

(C) three

(D) four

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Ans: (C)

 

Question :4 If v stands for velocity of sound, E is elasticity and d the density, then find x in the equation v = (d/E)^x

(A) 1

(B) ½

(C) 2

(D) -1/2

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Ans: (D)

 

Question :5 The multiplication of 10.610 with 0.210 upto correct number of significant figure is

(A) 2.2281

(B) 2.228

(C) 2.22

(D) 2.2

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Ans: (B)

 

Question :6  The measurement of radius of a circle has error of 1%. The error in measurement of its area is

(A) 1%

(B) 2%

(C) 3%

(D) none of these

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Ans: (B)

 

Question :7 Dimensional formula of latent heat

(A) M⁰L²T^-2

(B) MLT^-2

(C) ML²T^-2

(D) ML²T^-2

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Ans: (A)

 

Question :8  In case of measurement of ‘g’, if error in measurement of length of pendulum is 2%, the percentage error in time period is 1 %. The maximum error in measurement of g is

(A) 1 %

(B) 2 %

(C) 4 %

(D) no error

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Ans: (C)

 

Question :9 If length of pendulum is increased by 2%. The time period will

(A) increases by 1%

(B) decreases by 1%

(C) increases by 2%

(D) decreases by 2%

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Ans: (A)

 

Question :10  If radian correction is not considered in specific heat measurement. The measured value of specific heat will be

(A) more than its actual value.

(B) less than its actual value.

(C) remains same as actual value.

(D) none of these.

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Ans: (A)

 

Question :11 The S.I. unit of universal gas constant is

(A) Watt K^-1mol^-1

(B) N K^-1mol^-1

(C) J K^-1mol^-1

(D) erg K^-1mol^-1

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Ans: (C)

 

Question :12  The dimensional formula of couple

(A) ML²T^-2

(B)MLT^-1

(C) ML^-1T^-1

(D) M¹L¹T^-2

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Ans: (A)

 

Question :13 An experiment measures quantities a, b, c and x is calculated from $ \displaystyle x = \frac{a b^2}{c^3} $ . If the maximum percentage error in a, b and c are 1%, 3% and 2% respectively, the maximum percentage error in x will be

(A) 13%

(B) 17%

(C) 14%

(D) 11%

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Ans: (A)

 

Question :14 Dimensional formula of thermal conductivity is

(A) ML²T ^-3θ^-1

(B) ML²T ^-2θ^-4

(C) ML²T ^-2θ^-1

(D) MLT ^-3θ^-1

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Ans: (D)

 

Question :15  Three measurements 7.1 J , 7.2 J and 6.7 J are made as experiment the result with correct number of significant figures is

(A) 7.1 J

(B) 7.06 J

(C) 7.0 J

(D) 7 J

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Ans: (C)

 

Question :16  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^xQ^yc^z is dimensionless, may be

(A) x = 1, y =1, z = 1.

(B) x = 1, y =-1, z = 1.

(C) x = -1, y =1, z = 1.

(D) x = 1, y = 1, z = 1

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Ans: (B)

 

Question :17  A spherical ball of mass m and radius r is allowed to fall in a medium of viscosity η. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity is called time constant (τ). Dimensionally τ can be represented by

(A)$ \displaystyle \frac{m r^2}{6 \pi \eta} $

(B)$ \displaystyle \sqrt{\frac{6 \pi m r \eta}{g^2}} $

(C) $ \displaystyle \frac{m }{6 \pi \eta r } $

(D) none of these.

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Ans: (C)

 

Question :18 Which of the following is a possible dimensionless quantity ?

(A) Velocity gradient

(B) Pressure gradient

(C) Displacement gradient

(D) Force gradient

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Ans: (C)

 

Question :19 In specific resistance measurement of a wire using a meter bridge, the key k in the main circuit is kept open when we are not taking readings. The reason is

(A) the emf of cell will decrease.

(B) the value of resistance will change due to joule heating effect.

(C) the galvanometer will stop working.

(D) none of these.

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Ans: (B)

 

Question :20 In the experiment of verification of Ohm’s law the error in the current measurement is 1%, while that in the voltage measurement is 2%. The error in the resistance has a maximum value of

(A)1%

(B) 2%

(C) 3%

(D) none of these.

Click to See Answer :

Ans: (C)

 

Click to See All Answers :

1.C   2. C   3. C   4. D   5. B   6. B   7. A   8 C   9. A   10. A  

ANSWER:

11. C   12. A   13. A   14. D   15. C   16 B   17. C   18. C   19. B   20. C