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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 |
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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%
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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%
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The position of a particle at time $$t$$ is given by the relation $${x}({t})=\left(\frac{{v}_0}{\alpha}\right)\left(1-{e}^{-\alpha {t}}\right)$$, where $$v_0$$${}_{}$ is a constant and $$\alpha >0$$. The dimensions of $$v_0$$ and $$\alpha$$ are respectively:
1. $$\left[M^0L^{1}T^{-1}\right]~\text{and}~\left[T^{-1}\right]$$
2. $$\left[M^0L^{1}T^{0}\right]~\text{and}~\left[T^{-1}\right]$$
3. $$\left[M^0L^{1}T^{-1}\right]~\text{and}~\left[LT^{-1}\right]$$
4. $$\left[M^0L^{1}T^{-1}\right]~\text{and}~\left[T\right]$$

Subtopic: Â Dimensions |
Â 69%
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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 |
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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%
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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 |
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If force ($$F$$), velocity ($$\mathrm{v}$$), and time ($$T$$) are taken as fundamental units, the dimensions of mass will be:
1. $$[FvT^{-1}]$$
2. $$[FvT^{-2}]$$
3. $$[Fv^{-1}T^{-1}]$$
4. $$[Fv^{-1}T]$$

Subtopic: Â Dimensions |
Â 71%
From NCERT
AIPMT - 2014
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If dimensions of critical velocity $${v_c}$$ of a liquid flowing through a tube are expressed as $$\eta^{x}\rho^yr^{z}$$, where $$\eta, \rho~\text{and}~r$$ are the coefficient of viscosity of the liquid, the density of the liquid, and the radius of the tube respectively, then the values of $${x},$$ $${y},$$ and $${z},$$ respectively, will be:
1. $$1,-1,-1$$
2. $$-1,-1,1$$
3. $$-1,-1,-1$$
4. $$1,1,1$$

Subtopic: Â Dimensions |
Â 69%
From NCERT
NEET - 2015
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