Q. No.| 1. | both units and dimensions |
| 2. | units but no dimensions |
| 3. | dimensions but no units |
| 4. | no units and no dimensions |
The acceleration due to gravity on the surface of the Earth is \(g=10~\text{m/s}^2\) . The value in \(\text {km/minute}^2\) is:
| 1. | \(36\) | 2. | \(0.6\) |
| 3. | \(\dfrac{10}{6}\) | 4. | \(3.6\) |
| 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 \(a=0,\) \(b=-1,\) \(c=-2\) |
| 1. | \(\alpha t / \beta \) | 2. | \(\alpha \beta t \) |
| 3. | \(\alpha \beta / t \) | 4. | \(\beta t / \alpha\) |
IF \(P, Q\) and \(R\) are physical quantities, having different dimensions, which of the following combination/s can never be a meaningful quantity?
(a) \((P – Q)/R\)
(b) \(PQ – R\)
(c) \(PQ /R\)
(d) \((PR – Q^2)/R\)
(e) \((R + Q)/P\)
Choose the correct option:
1. (a), (e)
2. (a), (d), (e)
3. (a), (c), (d)
4. (b), (d)
Which of the following statements is incorrect?
| 1. | The dimensions of \(\beta\) are same as that of force. |
| 2. | The dimensions of \(\alpha^{-1}x\) are same as that of energy. |
| 3. | The dimensions of \(\eta^{-1} \sin \theta\) are same as that of \(\alpha \beta\). |
| 4. | The dimensions of \(\alpha\) same as that of \(\beta\). |
Given below are two statements:
| Assertion (A): | A dimensionally incorrect equation cannot ever be correct. |
| Reason (R): | Physically correct equations must be dimensionally correct. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
The velocity \(v\) of a particle at time \(t\) is given by \(v=at+\dfrac{b}{t+c}\), where \(a,\) \(b\) and \(c\) are constants. The dimensions of \(a,\) \(b\) and \(c\) are respectively:
1. \(\left[{LT}^{-2}\right],[{L}] \text { and }[{T}]\)
2. \( {\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]} \)
3. \( {\left[{LT}^2\right],[{LT}] \text { and }[{L}]} \)
4. \( {[{L}],[{LT}] \text { and }\left[{T}^2\right]}\)
In the \({RL}\) circuit shown in the figure, a resistor \(R\) and an inductor \(L\) are connected in series with an AC source. The impedance \(Z\) of the circuit is expressed as: \({Z}^2={A}^2+{B}^2.\)
(\(A\) and \(B\) represent two quantities associated with the circuit elements)
The dimensions of the product \({AB}\) are:
1. \(\left[{M^1 L^2 T}^2 A^{-3}\right] \)
2. \(\left[{M^2 L^4 T^{-6} A^{-4}}\right]\)
3. \(\left[{ML^{-1} T^2 A}^{-3}\right]\)
4. \(\left[{M^{-1} L^{-2}T}^2{A}^4\right]\)
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is/are not correct.
| (a) | \(y = a\sin \left(2\pi t / T\right)\) |
| (b) | \(y = a\sin(vt)\) |
| (c) | \(y = \left({\dfrac a T}\right) \sin \left({\dfrac t a}\right)\) |
| (d) | \(y = a \sqrt 2 \left(\sin \left({\dfrac {2 \pi t} T}\right) - \cos \left({\dfrac {2 \pi t} T}\right)\right)\) |
(Symbols have their usual meanings.)
Choose the correct option:
| 1. | (a), (c) |
| 2. | (a), (b) |
| 3. | (b), (c) |
| 4. | (a), (d) |
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