A physical quantity \(X\) depends on four measurables \(a\), \(b\), \(c\), and \(d\) as \(X = \frac{a^{2}b^{3}}{c^{5}d}.\) To ensure maximum accuracy in the determination of \(X\), the quantity that should be measured with maximum accuracy is:
1.  \(a\)
2.  \(b\)
3.  \(c\)
4.  \(d\)

Subtopic:  Errors |
 79%
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If z=A×BA+B, and errors in the determination of A and B are respectively A and B, then the fractional error in the calculation of z is :

1.  ΔAA+ΔBB+ΔA+ΔBA+B

2.  ΔAA+ΔBB(ΔA+ΔB)A+B

3.  ΔAA+ΔBB

4.  Zero

 

Subtopic:  Errors |
 71%
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Two resistors R1 = (3.0 ± 0.3) Ω and R2 = (5.0 ± 0.1) Ω  are connected in parallel. The equivalent resistance is :

1.  1.9±0.07 Ω2.   1.9±0.1 Ω3.  1.9±0.2 Ω4.  1.9±0.3 Ω

Subtopic:  Errors |
From NCERT
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Consider a dimensionally consistent equation given as :

P = ab + cde+f

Select the correct alternative.

1.  [ab]=[cd]2.  [a]=cdbe3.  [Pab]=cde+f4.  [b]=[P][e+f]

Subtopic:  Dimensions |
 65%
From NCERT
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A student performs an experiment to determine Young's modulus of a wire, exactly 1 m long by Searle's method. In a particular reading, the student measures extensions in the length of the wire to be 4.00 mm with an uncertainty of ± 0.01 mm at a load of exactly 1 kg. The student also measures the radius of wire to be 1.00 mm with an uncertainty of ± 0.005 mm. The Young's modulus obtained from the reading is (Take g = 10 m/s2) :
 
1.  (7.96 ± 0.10) × 108 N/m2

2.  (7.96±0.16)×108N/m2

3.  (8.0±0.2)×108N/m2

4.  (7.04±0.32)×108N/m2
Subtopic:  Errors |
From NCERT
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The main scale of a vernier calliper has \(n\) divisions/cm. \(n\) divisions of the vernier scale coincide with \((n-1)\) divisions of the main scale. The least count of the vernier calliper is:
1. \(\frac{1}{(n+1)(n-1)}\) cm
2. \(\frac{1}{n}\) cm
3. \(\frac{1}{n^{2}}\) cm
4. \(\frac{1}{(n)(n+1)}\) cm

Subtopic:  Measurement & Measuring Devices |
From NCERT
NEET - 2019
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A particle of mass 'm' is executing oscillations about the origin on the x-axis. Its potential energy is U(x) = k|x| where k is a positive constant. If the amplitude of oscillation is a, then its time period T is directly proportional to:

1.  a-1/2

2.  a 

3.  a1/2

4.  a0

Subtopic:  Dimensions |
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The dimension of uvmvdv is

(1) M1L-2T-2

(2) M1L2T-2

(3) [M1L1T-1]

(4) None of these

Subtopic:  Dimensions |
 69%
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In an experiment, the percentage errors that occurred in the measurement of physical quantities \(A,\) \(B,\) \(C,\) and \(D\) are \(1\%\), \(2\%\), \(3\%\), and \(4\%\) respectively. Then, the maximum percentage of error in the measurement of \(X,\) where \(X=\frac{A^2 B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^3}\), will be:
1. \(10\%\)
2. \(\frac{3}{13}\%\)
3. \(16\%\)
4. \(-10\%\)

Subtopic:  Errors |
 85%
From NCERT
NEET - 2019
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The unit of thermal conductivity is:

1. W m–1 K–1 2. J m K–1
3. J m–1 K–1 4. W m K–1
Subtopic:  Dimensions |
 58%
From NCERT
NEET - 2019
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