Units and Measurements Test

Result

Units and Measurements Test - 89

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Weekly Quiz Competition

Question 1
1 / -0

Characteristics of Scientific observation are.

A
Accuracy

B
Precision and objectivity

C
Systematic and recorded

D
All of the above

Solution
Question 2
1 / -0

The distance covered by a particle in time $$t$$ is given by$$ x = a + bt + ct^2 + dt^3$$. The dimensions of $$a$$ and $$d$$ are -

A
$$L,T^{-3}$$

B
$$L,LT^{-3}$$

C
$$L,T^{3}$$

D
None of these.

Solution
Question 3
1 / -0

A glass cube of edge 1 $$ {cm} $$ and $$ \mu=1.5 $$ has a spot at the centre .The area of the cube face that must be covered to prevent the spot from being seen is (in $ {cm}^{2} ) $

A
$$
\sqrt{5} \pi
$$

B
$$
5 \pi
$$

C
$$
\frac{\pi}{\sqrt{5}}
$$

D
$$
\frac{\pi}{5}
$$

Solution
Question 4
1 / -0

The mass of a bag is $$1.6kg$$. Two objects of mass $$20\,gm$$ and $$15\,gm$$ meausred to an accuracy of $$1gm$$ are added to it. The total mass of the bag calculated to the correct number of significant figures is

A
$$1.64\,kg$$

B
$$1.635\,kg$$

C
$$1.6\,kg$$

D
$$1.95\,kg$$

Solution
Question 5
1 / -0

Using mass (M), length (L), time(T) and current (A) as fundamental quantities,the dimension of permeability is

A
$$ [M^{-1} LT^{-2} A] $$

B
$$ [M^{-2} LT^{-2} A^{-1}] $$

C
$$ [MLT^{-2} A^{-2} ] $$

D
$$ [MLT^{-1} A^{-1} ] $$

Solution
Question 6
1 / -0

Suppose a quantity x can be dimensionally represented in terms of M, L and $$T$$ that is, $$[x]=M^aL^bT^c$$. The quantity mass.

A
Can always be dimensionally represented in terms of L, T and x

B
Can never be dimensionally represented in terms of L, T and x

C
May be represented in terms of L, T and x if $$a=0$$

D
May be represented in terms of L, T and x if $$a\neq 0$$

Solution
Question 7
1 / -0

Taking density $$(\rho)$$, velocity $$(v)$$ and area $$(a)$$ to be fundamental unit then the dimensions of force are:

A
$$[av^2\rho]$$

B
$$[a^2v\rho]$$

C
$$[av\rho^2]$$

D
$$[a^0v\rho]$$

Solution
Question 8
1 / -0

A body of mass $$m_{1}$$, moving with uniform velocity of $$40\ m/s$$ collides with another mass $$m_{2}$$ at rest and then the two together begin to move in a uniform velocity of $$30\ m/s$$. The ratio of their masses $$(m_{1}/m_{2})$$ is

A
$$0.75$$

B
$$1.33$$

C
$$3.0$$

D
$$4.0$$

Solution
Question 9
1 / -0

If area $$(A)$$, velocity $$(v)$$ and density $$(\rho)$$ are base units, then the dimensional formula of force can be represented

A
$$ \left [ Av\rho \right ] $$

B
$$ \left [ Av^{2}\rho \right ] $$

C
$$ \left [ Av\rho^{2} \right ] $$

D
$$ \left [ A^{2}v\rho \right ] $$

Solution
Question 10
1 / -0

Which of the following pairs of physical quantities does not have same dimensional formula?

A
Work and torque

B
Angular momentum and Plancks constant

C
Tension and surface tension

D
Impulse and linear momentum

Solution

a) Work =$$F \times \Delta x=[MLT^{-2}[L]=[ML^2T^{-2}]]$$

Torque=force $$\times$$ distance =$$[ML^2T^{-2}]$$

b) Angular momentum$$mvr=[M][LT^{1}][L]=[ML^2T^{-1}]$$

Plank's constant=$$\dfrac{E}{V}=\dfrac{[ML^2T^{-2}]}{[T^{-1}]}=[ML^2T^{-1}]$$

c) Tension (force)=$$[MLT^{-2}]$$

Surface tension =$$\dfrac{force}{length}=\dfrac{[MLT^{-2}]}{[L]}=[ML^0T^{-2}]$$

d) Impulse $$=F \times \Delta t=[MLT^{-2}][T]=[MLT^{-1}]$$

Momentum =$$mass \times velocity=[M][LT^{-1}]=[MLT^{-1}]$$

So, among the above pairs only tension and surface tension does not have the same dimensional formula. They both sound similar but they both have different meaning and different applications.