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If $$u_1$$ and $$u_2$$ are the units selected in two systems of measurement and $$n_1$$ and $$n_2$$ are their numerical values, then:

 1 $$n_1u_1=n_2u_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$$ 2 $$n_1u_1+n_2u_2=0$$ 3 $$n_1n_2=u_1u_2$$ 4 $$(n_1+u_1)=(n_2+u_2)$$
Subtopic: Â Dimensions |
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The velocity $$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 |
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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 |
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From NCERT
NEET - 2009
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The dimensional formula of pressure is:

 1 $$\left[MLT^{-2}\right]$$ 2 $$\left[ML^{-1}T^{2}\right]$$ 3 $$\left[ML^{-1}T^{-2}\right]$$ 4 $$\left[MLT^{2}\right]$$
Subtopic: Â Dimensions |
Â 80%
From NCERT
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The dimensional formula for impulse is:

 1 $$[MLT^{-2}]$$ 2 $$[MLT^{-1}]$$ 3 $$[ML^2T^{-1}]$$ 4 $$[M^2LT^{-1}]$$
Subtopic: Â Dimensions |
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From NCERT
PMT - 1991
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In the relation, $$y=a \cos (\omega t-k x)$$, the dimensional formula for $$k$$ will be:
1. $${\left[M^0 L^{-1} T^{-1}\right]}$$
2. $${\left[M^0 L T^{-1}\right]}$$
3. $${\left[M^0 L^{-1} T^0\right]}$$
4. $${\left[M^0 L T\right]}$$

Subtopic: Â Dimensions |
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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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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 |
Â 77%
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The dimensions of $$(\mu_0\varepsilon_0)^{\frac{-1}{2}}$$ are:
1. $$\left[L^{-1}T\right]$$
2. $$\left[LT^{-1}\right]$$
3. $$\left[L^{{-1/2}}T^{{1/2}}\right]$$
4. $$\left[L^{{-1/2}}T^{{-1/2}}\right]$$

Subtopic: Â Dimensions |
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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 |
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