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# If the dimensions of a physical quantity are given by ${\mathrm{}}^{}$$$[M^aL^bT^c],$$ then the physical quantity will be: 1. pressure if $$a=1, ~b=-1,~c=-2$$ 2. velocity if $$a=1,~b=0,~c=-1$$ 3. acceleration if $$a=1,~b=1,~c=-2$$ 4. force if $$a=0, ~b= -1,~c=-2$$

Subtopic: Â Dimensions |
Â 85%
From NCERT
NEET - 2009
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If the error in the measurement of the radius of a sphere is $$2\%$$, then the error in the determination of the volume of the sphere will be:

 1 $$4\%$$ 2 $$6\%$$ 3 $$8\%$$ 4 $$2\%$$
Subtopic: Â Errors |
Â 84%
From NCERT
NEET - 2008
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The pitch of a screw gauge is $$1~$$mm and there are $$100$$ divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads $$1$$ mm and $$47$$th division on the circular scale coincides with the reference line. The length of the wire is $$5.6$$ cm. Curved surface area (in cm2) of the wire in appropriate number of significant figures will be:

1. $$2.4$$ cm2

2. $$2.56$$ cm2

3. $$2.6$$ cm2

4. $$2.8$$ cm2

Subtopic: Â Measurement & Measuring Devices |
Â 55%
From NCERT
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When units of mass, length, and time are taken as $$10~\text{kg}, 60~\text{m}~\text{and}~60~\text{s}$$ respectively, the new unit of energy becomes $$x$$ times the initial SI unit of energy. The value of $$x$$ will be:
1. $$10$$
2. $$20$$
3. $$60$$
4. $$120$$

Subtopic: Â Dimensions |
Â 75%
From NCERT
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Which of the following relations is dimensionally wrong? [The symbols have their usual meanings]
1. $$s= ut+\frac{1}{6}at^2$$
2. $$v^2= u^2+\frac{2as^2}{\pi}$$
3. $$v= u-2at$$
4. All of these

Subtopic: Â Dimensions |
Â 67%
From NCERT
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In which of the following, the number of significant figures is different from that in the others?

 1 $$2.303~\text{kg}$$ 2 $$12.23~\text{m}$$ 3 $$0.002\times10^{5}~\text{m}$$ 4 $$2.001\times10^{-3}~\text{kg}$$
Subtopic: Â Significant Figures |
Â 89%
From NCERT
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A thin wire has a length of $$21.7~\text{cm}$$ and a radius of $$0.46~\text{mm}$$. The volume of the wire to correct significant figures is:

 1 $$0.15~ \text{cm}^3$$ 2 $$0.1443~ \text{cm}^3$$ 3 $$0.14~ \text{cm}^3$$ 4 $$0.144 ~\text{cm}^3$$
Subtopic: Â Significant Figures |
Â 64%
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If $${x}=\frac{{a} \sin \theta+{b} \cos \theta}{{a}+{b}},$$ then:

 1 the dimensions of $$x$$ and $$a$$ must be the same 2 the dimensions of $$a$$ and $$b$$ are not the same 3 $$x$$ is dimensionless 4 none of the above

Subtopic: Â Dimensions |
Â 64%
From NCERT
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For the expression, $$10^{(at+3)}$$, the dimensions of $$a$$ will be:
1. $$\left[M^0L^0T^{0}\right]$$
2. $$\left[M^0L^0T^{1}\right]$$
3. $$\left[M^0L^0T^{-1}\right]$$
4. None of these

Subtopic: Â Dimensions |
Â 72%
From NCERT
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A screw gauge has the least count of $$0.01~\text{mm}$$ and there are $$50$$ divisions in its circular scale. The pitch of the screw gauge is:

 1 $$0.25$$ mm 2 $$0.5$$ mm 3 $$1.0$$ mm 4 $$0.01$$ mm
Subtopic: Â Measurement & Measuring Devices |
Â 85%
From NCERT
NEET - 2020
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