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# The length and breadth of a rectangular sheet are $$16.2$$ cm and $$10.1$$ cm, respectively. The area of the sheet in appropriate significant figures and error would be, respectively, 1. $$164\pm3~\text{cm}^2$$ 2. $$163.62\pm2.6~\text{cm}^2$$ 3. $$163.6\pm2.6~\text{cm}^2$$ 4. $$163.62\pm3~\text{cm}^2$$

Subtopic:  Errors | Significant Figures |
61%
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Which of the following pairs of physical quantities does not have the same dimensional formula?

 1 work and torque 2 angular momentum and Planck's constant 3 tension and surface tension 4 impulse and linear momentum

Subtopic:  Dimensions |
74%
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The measure of two quantities along with the precision of respective measuring instrument is . The value of AB will be:

1. (0.25 $±$ 0.08) m

2. (0.25 $±$ 0.5) m

3. (0.25 $±$ 0.05) m

4. (0.25 $±$ 0.135) m

Subtopic:  Errors |
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You measure two quantities as A = 1.0 m $±$ 0.2 m, B = 2.0 m $±$ 0.2 m. We should report the correct value for $\sqrt{\mathrm{AB}}$ as

1. 1.4 m $±$ 0.4 m

2. 1.41 m $±$ 0.15 m

3. 1.4 m $±$ 0.3 m

4. 1.4 m $±$ 0.2 m

Subtopic:  Errors |
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Which of the following measurement is most precise?
1. $$5.00$$ mm
2. $$5.00$$ cm
3. $$5.00$$ m
4. $$5.00$$ km

Subtopic:  Errors |
83%
From NCERT
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The mean length of an object is $$5~\text{cm}$$. Which of the following measurements is the most accurate?

 1 $$4.9~\text{cm}$$ 2 $$4.805~\text{cm}$$ 3 $$5.25~\text{cm}$$ 4 $$5.4~\text{cm}$$
Subtopic:  Errors |
80%
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Young's modulus of steel is $$1.9 \times 10^{11} ~\text{N/m}^2$$. When expressed in CGS units of $$\text{dyne/cm}^2$$, it will be equal to: $$(1 \mathrm{~N}=10^5 \text { dyne, } 1~ \text{m}^2=10^4 ~\text{cm}^2)$$
1. $$1.9 \times 10^{10}$$
2. $$1.9 \times 10^{11}$$
3. $$1.9 \times 10^{12}$$
4. $$1.9 \times 10^9$$

Subtopic:  Dimensions |
73%
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If momentum ($${p}$$), area ($${A}$$), and time ($${T}$$) are taken to be fundamental quantities, then energy has the dimensional formula:
 1 $${\left[{pA}^{-1} {~T}^1\right]}$$ 2 $${\left[{p}^2 {AT}\right]}$$ 3 $${\left[{pA}^{-1 / 2} {~T}\right]}$$ 4 $${\left[{pA}^{1 / 2} {~T}^{-1}\right]}$$
Subtopic:  Dimensions |
76%
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On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is/are not correct.

 (a) $$y = a\sin \left(2\pi t / T\right)$$ (b) $$y = a\sin(vt)$$ (c) $$y = \left({\dfrac a T}\right) \sin \left({\dfrac t a}\right)$$ (d) $$y = a \sqrt 2 \left(\sin \left({\dfrac {2 \pi t} T}\right) - \cos \left({\dfrac {2 \pi t} T}\right)\right)$$

(Symbols have their usual meanings.)
Choose the correct option:

 1 (a), (c) 2 (a), (b) 3 (b), (c) 4 (a), (d)

Subtopic:  Dimensions |
63%
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IF $$P, Q$$ and $$R$$ are physical quantities, having different dimensions, which of the following combination/s can never be a meaningful quantity?

(a) $$(P – Q)/R$$
(b) $$PQ – R$$
(c) $$PQ /R$$
(d) $$(PR – Q^2)/R$$
(e) $$(R + Q)/P$$

Choose the correct option:
1. (a), (e)
2. (a), (d), (e)
3. (a), (c), (d)
4. (b), (d)

Subtopic:  Dimensions |
55%
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