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# If the units of force and length, is increased by four times, then the unit of energy increases by: 1. 16 times 2. 8 times 3. 2 times 4. 4 times

Subtopic: Â Dimensions |
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The velocity $$v$$ of a particle at time $$t$$ is given by $${v}={at}+\frac{{b}}{{t}+{c}}.$$ The dimensions of $${a}$$, $${b}$$, and $${c}$$ are respectively:
1. $${\left[{LT}^{-2}\right],[{L}],[{T}]}$$
2. $${\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]}$$
3. $${\left[{LT}^2\right],[{LT}] \text { and }[{L}]}$$
4. $${[{L}],[{LT}], \text { and }\left[{T}^2\right]}$$

Subtopic: Â Dimensions |
Â 85%
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If $$97.52$$ is divided by $$2.54$$, the correct result in terms of significant figures is:

 1 $$38.4$$ 2 $$38.3937$$ 3 $$38.394$$ 4 $$38.39$$
Subtopic: Â Significant Figures |
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A physical quantity $$A$$ is related to four observable quantities $$a$$, $$b$$, $$c$$ and $$d$$ as follows, $$A= \frac{a^2b^3}{c\sqrt{d}},$$ the percentage errors of measurement in $$a$$, $$b$$, $$c$$ and $$d$$ are $$1\%$$, $$3\%$$, $$2\%$$ and $$2\%$$ respectively. The percentage error in quantity $$A$$ will be:
1. $$12\%$$
2. $$7\%$$
3. $$5\%$$
4. $$14\%$$

Subtopic: Â Errors |
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The number of significant figures in the numbers $$25.12,$$ $$2009,$$ $$4.156$$ and $$1.217\times 10^{-4}$$ is:

 1 $$1$$ 2 $$2$$ 3 $$3$$ 4 $$4$$
Subtopic: Â Significant Figures |
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A physical quantity $$P$$ is given by $$P=\dfrac{A^3 B^{1/2}}{C^{-4}D^{3/2}}.$$ The quantity which contributes the maximum percentage error in $$P$$ is:

 1 $$A$$ 2 $$B$$ 3 $$C$$ 4 $$D$$
Subtopic: Â Errors |
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The length of a cylinder is measured with a meter rod having the least count of $$0.1~\text{cm}$$. Its diameter is measured with vernier callipers having the least count of $$0.01~\text{cm}$$. Given that the length is $$5.0~\text{cm}$$ and the radius is $$2.0~\text{cm}$$. The percentage error in the calculated value of the volume will be:

 1 $$1\%$$ 2 $$2\%$$ 3 $$3\%$$ 4 $$4\%$$
Subtopic: Â Errors |
Â 63%
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The periods of oscillation of a simple pendulum in an experiment are recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s, and 2.80 s respectively. The average absolute error will be:

1. 0.1 s

2. 0.11 s

3. 0.01 s

4. 1.0 s

Subtopic: Â Errors |
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The decimal equivalent of $$\frac{1}{20}$$ up to three significant figures is:

 1 $$0.0500$$ 2 $$0.05000$$ 3 $$0.0050$$ 4 $$5.0 \times 10^{-2}$$
Subtopic: Â Significant Figures |
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The percentage errors in the measurement of mass and speed are $$2\%$$ and $$3\%$$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed:

 1 $$11\%$$ 2 $$8\%$$ 3 $$5\%$$ 4 $$1\%$$
Subtopic: Â Errors |
Â 85%
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