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 $\mathrm{m}/{\mathrm{s}}^{2}$) :

Subtopic:  Errors |
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NEET 2022 - Target Batch - Aryan Raj Singh
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NEET 2022 - Target Batch - Aryan Raj Singh

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Subtopic:  Significant Figures |
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NEET 2022 - Target Batch - Aryan Raj Singh
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NEET 2022 - Target Batch - Aryan Raj Singh

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A spherical body of mass m and radius r is allowed to fall in a medium of viscosity $\eta$. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity $\left(v\right)$ is called time constant $\left(\tau \right)$. Dimensionally $\tau$ can be represented by

(1) $\frac{m{r}^{2}}{6\pi \eta }$

(b) $\sqrt{\left(\frac{6\pi mr\eta }{{g}^{2}}\right)}$

(c) $\frac{m}{6\pi \eta rv}$

(4) None of the above

Subtopic:  Dimensions |
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NEET 2022 - Target Batch - Aryan Raj Singh
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NEET 2022 - Target Batch - Aryan Raj Singh

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The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type $f=C\text{\hspace{0.17em}}{m}^{x}{K}^{y}$; where C is a dimensionless quantity. The value of x and y are

(1) $x=\frac{1}{2},\text{\hspace{0.17em}}y=\frac{1}{2}$

(2) $x=-\frac{1}{2},\text{\hspace{0.17em}}y=-\frac{1}{2}$

(3) $x=\frac{1}{2},\text{\hspace{0.17em}}y=-\frac{1}{2}$

(4) $x=-\frac{1}{2},\text{\hspace{0.17em}}y=\frac{1}{2}$

Subtopic:  Dimensions |
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NEET 2022 - Target Batch - Aryan Raj Singh
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NEET 2022 - Target Batch - Aryan Raj Singh

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The quantities A and B are related by the relation, m = A/B, where m is the linear density and A is the force. The dimensions of B are of

(1) Pressure

(2) Work

(3) Latent heat

(4) None of the above

Subtopic:  Dimensions |
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NEET 2022 - Target Batch - Aryan Raj Singh
To view explanation, please take trial in the course below.
NEET 2022 - Target Batch - Aryan Raj Singh

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The velocity of water waves $v$ may depend upon their wavelength $\lambda$, the density of water $\rho$ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as

(1) ${v}^{2}\propto g{\lambda }^{-1}{\rho }^{-1}$

(2) ${v}^{2}\propto g\lambda \rho$

(3) ${v}^{2}\propto g\lambda$

(4) ${v}^{2}\propto {g}^{-1}{\lambda }^{-3}$

Subtopic:  Dimensions |
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NEET 2022 - Target Batch - Aryan Raj Singh
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NEET 2022 - Target Batch - Aryan Raj Singh

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The equation of a wave is given by $Y=A\mathrm{sin}\omega \left(\frac{x}{v}-k\right)$ where $\omega$ is the angular velocity, x is length and $v$ is the linear velocity. The dimension of k is

(1) LT

(2) T

(3) ${T}^{-1}$

(4) T2

Subtopic:  Dimensions |
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NEET 2022 - Target Batch - Aryan Raj Singh
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NEET 2022 - Target Batch - Aryan Raj Singh

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The period of a body under SHM i.e. presented by $T={P}^{a}{D}^{b}{S}^{c}$; where P is pressure, D is density and S is surface tension. The value of a, b and c are

(1) $-\frac{3}{2},\text{\hspace{0.17em}}\frac{1}{2},\text{\hspace{0.17em}}1$

(2) $-1,\text{\hspace{0.17em}}-2,\text{\hspace{0.17em}}3$

(3) $\frac{1}{2},\text{\hspace{0.17em}}-\frac{3}{2},\text{\hspace{0.17em}}-\frac{1}{2}$

(4) $1,\text{\hspace{0.17em}}2,\text{\hspace{0.17em}}\frac{1}{3}$

Subtopic:  Dimensions |
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NEET 2022 - Target Batch - Aryan Raj Singh
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The velocity of a freely falling body changes as ${g}^{p}{h}^{q}$ where g is acceleration due to gravity and h is the height. The values of p and q are

(1) $1,\frac{1}{2}$

(2) $\frac{1}{2},\frac{1}{2}$

(3) $\frac{1}{2},\text{\hspace{0.17em}}1$

(4) 1, 1

Subtopic:  Dimensions |
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NEET 2022 - Target Batch - Aryan Raj Singh
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NEET 2022 - Target Batch - Aryan Raj Singh

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A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time the velocity of the ball attains a constant value known as terminal velocity ${v}_{T}$. The terminal velocity depends on (i) the mass of the ball m, (ii) $\eta$, (iii) r and (iv) acceleration due to gravity g. Which of the following relations is dimensionally correct

(1) ${v}_{T}\propto \frac{mg}{\eta r}$

(2) ${v}_{T}\propto \frac{\eta r}{mg}$

(3) ${v}_{T}\propto \eta rmg$

(4) ${v}_{T}\propto \frac{mgr}{\eta }$

Subtopic:  Dimensions |
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NEET 2022 - Target Batch - Aryan Raj Singh
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NEET 2022 - Target Batch - Aryan Raj Singh

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