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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 |
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In a vernier calliper, $$N$$ divisions of vernier scale coincide with ($$N\text-1$$) divisions of the main scale (in which the length of one division is $$1$$ mm). The least count of the instrument should be:
1. $$N~\text{mm}$$
2. $$(N-1)~\text{mm}$$
3. $$\frac{1}{10N}~\text{cm}$$
4. $$\frac{1}{(N-1)}~\text{mm}$$

Subtopic: Â Measurement & Measuring Devices |
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In certain vernier callipers, $$25$$ divisions on the vernier scale have the same length as $$24$$ divisions on the main scale. One division on the main scale is $$1$$ mm long. The least count of the instrument is:

 1 $$0.04$$ mm 2 $$0.01$$ mm 3 $$0.02$$ mm 4 $$0.08$$ mm
Subtopic: Â Measurement & Measuring Devices |
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Consider a screw gauge without any zero error. What will be the final reading corresponding to the final state as shown?
It is given that the circular head translates $$P$$ MSD in $${N}$$ rotations. ($$1$$ MSD $$=$$ $$1~\text{mm}$$.)

1. $$\left(\frac{{P}}{{N}}\right)\left(2+\frac{45}{100}\right) \text{mm}$$
2. $$\left(\frac{{N}}{{P}}\right)\left(2+\frac{45}{{N}}\right) \text{mm}$$
3. $$P\left(\frac{2}{{N}}+\frac{45}{100}\right) \text{mm}$$
4. $$\left(2+\frac{45}{100} \times \frac{{P}}{{N}}\right) \text{mm}$$

Subtopic: Â Measurement & Measuring Devices |
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The main scale reading is $$-1$$ mm when there is no object between the jaws. In the vernier calipers, $$9$$ main scale division matches with $$10$$ vernier scale divisions. Assume the edge of the Vernier scale as the '0' of the vernier. The thickness of the object using the defected vernier calipers will be:

1. $$12.2~\text{mm}$$
2. $$1.22~\text{mm}$$
3. $$12.3~\text{mm}$$
4. $$12.4~\text{mm}$$

Subtopic: Â Measurement & Measuring Devices |
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Planck's constant ($$h$$), speed of light in the vacuum ($$c$$), and Newton's gravitational constant ($$G$$) are the three fundamental constants. Which of the following combinations of these has the dimension of length?

 1 $$\frac{\sqrt{hG}}{c^{3/2}}$$ 2 $$\frac{\sqrt{hG}}{c^{5/2}}$$ 3 $$\frac{\sqrt{hG}}{G}$$ 4 $$\frac{\sqrt{Gc}}{h^{3/2}}$$
Subtopic: Â Dimensions |
Â 70%
From NCERT
NEET - 2016
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A student measured the diameter of a small steel ball using a screw gauge of least count $$0.001$$ cm. The main scale reading is $$5$$ mm and zero of circular scale division coincides with $$25$$ divisions above the reference level. If the screw gauge has a zero error of $$-0.004$$ cm, the correct diameter of the ball is:

 1 $$0.521$$ cm 2 $$0.525$$ cm 3 $$0.053$$ cm 4 $$0.529$$ cm
Subtopic: Â Measurement & Measuring Devices |
Â 65%
From NCERT
NEET - 2018
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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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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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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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