Part-3 Units and measurement Hard

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The heat dissipated (l²Rt) in a resistance can be obtained by the measurement of resistance, current and time. If the maximum percentage error in the measurement of these quantities is 1%, 2%, and 1% respectively. The maximum percentage error in the determination of the dissipated heat is 002D

4%

6%

4/3%

2%

A cube has a side 1.2 × 10–² Its volume will be recorded as -

1.728 × 10–6 m³

1.72 × 10–6 m³

1.7 × 10–6 m³

.72 × 10–6 m³

If energy (E), velocity (v) and force (F), be taken as fundamental quantities, then what are the dimensions of mass

EV²

EV–²

FV–¹

FV–²

If x = at + bt2, where x is in metres and t in hours (hr), then unit of b will be -

m²/hr

M

m/hr

m/hr²

The percentage error in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum percentage error in the estimate of kinetic energy obtained by measuring mass and speed -

11%

8%

5%

4%

A wire is of mass (0.3 ± .003) gm. The radius is (0.5 ± 0.005) cm and length is (6 ± .06) cm. The maximum percentage error in density is -

3%

4%

8%

16%

[ML²T^–3A^–2] is the dimensional formula of -

Electric resistance

Capacity

Electric potential

Specific resistance

If energy E, velocity V and time t are chosen as fundamental quantities, then the dimensional formula of surface tension is

[EV^–2T^–2]

[EV^–1T^–2]

[EV^–2T^–1]

[E²V^–1T^–2]

The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by relation of the type f = cm^xk^y,where c is a dimensional constant. The value of x and y are-

1/2, ½

– 1/2, – ½

1/2, – ½

– 1/2, ½

Which of the following measurement is most accurate?

9 × 10^–2 m

90 × 10^–3 m

900 × 10^–4 m

0.090 m

Two rods with lengths 20.123 cm and 18.1 cm are placed side by side. The difference in their lengths is -

2 cm

2.0 cm

2.02 cm

2.023 cm

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 -

1%

2%

6%

8%

Which of the following groups has different dimensions?

Potential difference, emf, voltage

Pressure, stress, Young’s modulus

Heat, energy, work done

Dipole moment, electric flux, electric field

Which of the following is not the name of a physical quantity

Kilogram

Impulse

Energy

Ensity

The energy E radiated per unit area per second by a black body at temperature T is given byE = σT⁴, where σ is the Stefan's constant. The dimensions of s are -

MT²K^–2

MT^–3K^–4

MT³K^–4

ML⁴T^–3K^–4

Match the following columns–

Column-I Column-II

(a) GM_eM_s(p) (kgm)(mtr)³(sec)^–2

(b)3RT/ M (q) (mtr)²(sec)^–2

a→q, b →p

a → p, b→ q

a→ p, b →p

a→p, b → p

The length, breadth and thickness of a strip are: (10.0 ± 0.1) cm, (1.00 ± 0.01) cm and (0.100 ± 0.001) cm respectively. The most probable error in its volume will be:

± 0. 111 cm³

± 0.012 cm³

± 0.03 cm³

None of these

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

ML²T^–1 and MLT^–1

ML²T^–1 and ML²T^–1

MLT^–1 and ML²T^–1

MLT^–1 and ML²T^–2

The product of pressure and volume have the same units as the product of :

Charge and potential

Electric field strength and distance

Electromotive force and capacitance

Magnetic moment and magnetic induction

Dimensions of specific resistance are -

ML³T^–3A^–2

ML^–3T³A^–2

ML³T³A^–2q

None

Which of the following is unit less quantity?

Velocity gradient

Pressure gradient

Displacement gradient

Force gradient

Match the following:

Column-I Column-II

(A) Coefficient of viscosity (p) M²L^–1T^–2

(B) Surface Tension (q) MLºT^–2

(C) Modulus of rigidity (r) ML^–1T^–2

(D) Energy per unit volume of fluid (s) None

(A) s, (B) q, (C) r, (D) r

(A) r, (B) q, (C) r, (D) s

(A) s, (B) r, (C) q, (D) r

(A) r, (B) r, (C) q, (D) s

Dimensional formula for the linear momentum is-

[ML⁰T^–1]

[M⁰LT^–1]

[MLT^–1]

[ML^–1T]

Dimensional formula for the Planck's constant is -

[ML²T]

[ML²T^–1]

[M²LT^–1]

[M^–1L²T^–1]

Dimensional formula for the gravitational constant is-

[M^–1L³T^–2]

[M^–1L²T^–3]

[M^–1LT^–2]

[M^–2L³T^–1]

Part-3 Units and measurement Hard

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