The dimensional formula of the coefficient of thermal conductivity is :

1.  $\left[{\mathrm{M}}^{1}{\mathrm{L}}^{1}{\mathrm{T}}^{-3}{\mathrm{K}}^{-1}\right]$

2.  $\left[{\mathrm{M}}^{3}{\mathrm{L}}^{-1}{\mathrm{T}}^{-3}\mathrm{K}\right]$

3.  $\left[{\mathrm{M}}^{1}{\mathrm{L}}^{-3}{\mathrm{T}}^{-1}{\mathrm{K}}^{-1}\right]$

4.  $\left[{\mathrm{M}}^{1}{\mathrm{L}}^{1}{\mathrm{T}}^{-3}\mathrm{K}\right]$

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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Subtopic:  Significant Figures |

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A physical parameter 'a' can be determined by measuring the parameters b,  and  using the relation, $\mathrm{a}=\frac{{\mathrm{b}}^{\mathrm{\alpha }}{\mathrm{c}}^{\mathrm{\beta }}}{{\mathrm{d}}^{\mathrm{\gamma }}{\mathrm{e}}^{\mathrm{\delta }}}$. If the maximum errors in the measurement of b, c,  and e

Subtopic:  Errors |

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The unit of angular acceleration in the SI system is

(1) $N\text{\hspace{0.17em}}k{g}^{-1}$

(2) $m\text{\hspace{0.17em}}{s}^{-2}$

(3) $rad\text{\hspace{0.17em}}{s}^{-2}$

(4) $m\text{\hspace{0.17em}}k{g}^{-1}K$

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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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 |
To view explanation, please take trial in the course below.
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 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. $x=-\frac{1}{2},y=-\frac{1}{2}$

3. $x=\frac{1}{2},y=-\frac{1}{2}$

4. $x=-\frac{1}{2},y=\frac{1}{2}$

Subtopic:  Dimensions |
To view explanation, please take trial in the course below.
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 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 |
To view explanation, please take trial in the course below.
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. ${\mathrm{v}}^{2}\propto {\mathrm{g\lambda }}^{-1}{\mathrm{\rho }}^{-1}$

2. ${\mathrm{v}}^{2}\propto \mathrm{g\lambda \rho }$

3. ${\mathrm{v}}^{2}\propto \mathrm{g\lambda }$

4. ${\mathrm{v}}^{2}\propto {\mathrm{g}}^{-1}{\mathrm{\lambda }}^{-3}$

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

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The period of a body under SHM is presented by $\mathrm{T}={\mathrm{P}}^{\mathrm{a}}{\mathrm{D}}^{\mathrm{b}}{\mathrm{S}}^{\mathrm{c}}$; 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)

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

Difficulty Level: