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Q. No.A balloon is made of a material of surface tension \(S\) and its inflation outlet (from where gas is filled in it) has small area \(A.\) It is filled with a gas of density \(\rho\) and takes a spherical shape of radius \(R.\) When the gas is allowed to flow freely out of it, its radius \(r\) changes from \(R\) to \(0\) (zero) in time \(T.\) If the speed \(v(r)\) of gas coming out of the balloon depends on \(r\) as \(r^a\) and \(T \propto S^\alpha A^\beta \rho^\gamma R^\delta\) then:
| 1. | \(a=-\dfrac{1}{2},~ \alpha=-\dfrac{1}{2}, ~\beta=-1, ~\gamma=\dfrac{1}{2},~ \delta=\dfrac{7}{2}\) |
| 2. | \(a=\dfrac{1}{2},~\alpha=\dfrac{1}{2},~ \beta=-\dfrac{1}{2}, ~\gamma=\dfrac{1}{2},~ \delta=\dfrac{7}{2}\) |
| 3. | \(a=\dfrac{1}{2}, ~\alpha=\dfrac{1}{2}, ~\beta=-1, ~\gamma=+1, ~\delta=\dfrac{3}{2}\) |
| 4. | \(a=-\dfrac{1}{2}, ~\alpha=-\dfrac{1}{2}, ~\beta=-1, ~\gamma=-\dfrac{1}{2}, ~\delta=\dfrac{5}{2}\) |
Subtopic: Dimensions |
From NCERT
NEET - 2025
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A physical quantity \(P\) is related to four observations \(a,b,c\) and \(d\) as follows:
\(P=\dfrac{a^3b^2}{c\sqrt{d}}\)
The percentage errors of measurement in \(a,b,c\) and \(d\) are \(1\%,3\%,2\%\) and \(4\%\) respectively. The percentage error in the quantity \(P\) is:
1. \(13\%\)
2. \(15\%\)
3. \(10\%\)
4. \(2\%\)
\(P=\dfrac{a^3b^2}{c\sqrt{d}}\)
The percentage errors of measurement in \(a,b,c\) and \(d\) are \(1\%,3\%,2\%\) and \(4\%\) respectively. The percentage error in the quantity \(P\) is:
1. \(13\%\)
2. \(15\%\)
3. \(10\%\)
4. \(2\%\)
Subtopic: Errors |
82%
From NCERT
NEET - 2025
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Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its \(10\) Vernier Scale Divisions (V.S.D.) are equal to its \(9\) Main Scale Divisions (M.S.D.). The least division in the M.S. is \(0.1\text{ cm}\) and the zero of V.S. is at \(x=0.1~ \text{cm}\) when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is \({M}=5~\text{cm}\) and the number of coinciding vernier division is \(8 ,\) the measured diameter after zero error correction, is:
1. \(4.98 ~\text{cm}\)
2. \(5.00 ~\text{cm}\)
3. \(5.18 ~\text{cm}\)
4. \(5.08 ~\text{cm}\)
1. \(4.98 ~\text{cm}\)
2. \(5.00 ~\text{cm}\)
3. \(5.18 ~\text{cm}\)
4. \(5.08 ~\text{cm}\)
Subtopic: Measurement & Measuring Devices |
From NCERT
NEET - 2025
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The quantities which have the same dimensions as those of solid angle are:
1. stress and angle
2. strain and arc
3. angular speed and stress
4. strain and angle
1. stress and angle
2. strain and arc
3. angular speed and stress
4. strain and angle
Subtopic: Dimensions |
63%
From NCERT
NEET - 2024
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In a vernier callipers, \((N+1)\) divisions of the vernier scale coincide with \(N\) divisions of the main scale. If \(1\) \(\text{MSD}\) represents \(0.1~\text{mm}\), the vernier constant (in \(\text{cm}\)) is:
| 1. | \(\dfrac{1}{100(N+1)} \) | 2. | \(100N\) |
| 3. | \(10(N+1) \) | 4. | \(\dfrac{1}{10 N}\) |
Subtopic: Measurement & Measuring Devices |
71%
From NCERT
NEET - 2024
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A force defined by; \(F = \alpha t^2 + \beta t\) acts on a particle at a given time \(t.\) The factor which is dimensionless, if \(\alpha\) and \(\beta\) are constants, is:
| 1. | \(\alpha t / \beta \) | 2. | \(\alpha \beta t \) |
| 3. | \(\alpha \beta / t \) | 4. | \(\beta t / \alpha\) |
Subtopic: Dimensions |
65%
From NCERT
NEET - 2024
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The percentage errors in the measurement of mass and momentum of an object are \(1\%\) and \(2\%\) respectively. The percentage error in the measurement of kinetic energy of the object will be:
| 1. | \(1\%\) | 2. | \(3\%\) |
| 3. | \(4\%\) | 4. | \(5\%\) |
Subtopic: Errors |
66%
From NCERT
NEET - 2024
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Match List- I with List- II.
Choose the correct answer from the options given below:
| List-I (Measured values) |
List-II (Significant figures) |
||
| A. | \(0.001213\) | I. | \(2\) |
| B. | \(2.1 \times 10^{16} \) | II. | \(3\) |
| C. | \(3.70\) | III. | \(1\) |
| D. | \(3000\) | IV. | \(4\) |
| 1. | A-III, B-II, C-I, D-IV | 2. | A-III, B-I, CII, D-IV |
| 3. | A-I, B-II, C-IV, D-III | 4. | A-IV, B-I, C-II, D-III |
Subtopic: Significant Figures |
86%
From NCERT
NEET - 2024
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A vernier calipers has \(1~\text{mm}\) marks on the main scale. It has \(20\) equal divisions on the vernier scale which match with \(16\) main scale divisions. The least count of this vernier calipers is:
1. \(0.02~\text{mm}\)
2. \(0.05~\text{mm}\)
3. \(0.10~\text{mm}\)
4. \(0.20~\text{mm}\)
1. \(0.02~\text{mm}\)
2. \(0.05~\text{mm}\)
3. \(0.10~\text{mm}\)
4. \(0.20~\text{mm}\)
Subtopic: Measurement & Measuring Devices |
70%
From NCERT
NEET - 2024
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The pitch of an error-free screw gauge is \(1~\text{mm},\) and there are \(100\) divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads \(1~\text{mm},\) and \(63^\text{rd}\) division on the circular scale coincides with the reference line. The diameter of the wire is:
| 1. | \(1.63 ~\text{cm}\) | 2. | \(0.163 ~\text{cm}\) |
| 3. | \(0.163~\text m\) | 4. | \(1.63 ~\text m\) |
Subtopic: Measurement & Measuring Devices |
72%
From NCERT
NEET - 2024
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