The dimensions of $\frac{a}{b}$ in the equation $P=\frac{a-{t}^{2}}{bx}$, where P is pressure, x is distance and t is time, are

(1) MT–2

(2) M2LT–3

(3) ML3T–1

(4) LT–3

Concept Questions :-

Dimensions
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Difficulty Level:

Dimensions of $\frac{1}{{\mu }_{0}{\epsilon }_{0}}$, where symbols have their usual meaning, are

(1) [LT–1]

(2) [L–1T]

(3) [L–2T2]

(4) [L2T–2]

Concept Questions :-

Dimensions
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Difficulty Level:

The dimensions of ${e}^{2}/4\pi {\epsilon }_{0}hc$, where $e,\text{\hspace{0.17em}}{\epsilon }_{0},\text{\hspace{0.17em}}h$ and c are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively

(1) $\left[{M}^{0}{L}^{0}{T}^{0}\right]$

(2) $\left[{M}^{1}{L}^{0}{T}^{0}\right]$

(3) $\left[{M}^{0}{L}^{1}{T}^{0}\right]$

(4) $\left[{M}^{0}{L}^{0}{T}^{1}\right]$

Concept Questions :-

Dimensions
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Difficulty Level:

If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be

(1) $3+6.01×\frac{100}{5.3}$

(2) $\frac{1}{3}×0.01×\frac{100}{5.3}$

(3) $\left(\frac{3×0.1}{5.3}\right)×100$

(4) $\frac{0.1}{5.3}×100$

Concept Questions :-

Errors
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Difficulty Level:

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is

(1) 1%

(2) 2%

(3) 6%

(4) 8%

Concept Questions :-

Errors
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Difficulty Level:

While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation $g=4{\pi }^{2}\left(l/{T}^{2}\right)$ will be

(1) 2%

(2) 4%

(3) 7%

(4) 10%

Concept Questions :-

Errors
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Difficulty Level:

The length, breadth, and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm The volume of the block according to the idea of significant figures should be

(1) 1 × 102 cm3

(2) 2 × 102 cm3

(3) 1.763 × 102 cm3

(4) None of these

Concept Questions :-

Significant Figures
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Difficulty Level:

The position of a particle at time t is given by the relation  , where v0 is a constant and α > 0. The dimensions of v0 and α are respectively

(1) ${M}^{0}{L}^{1}{T}^{-1}$ and T–1

(2) ${M}^{0}{L}^{1}{T}^{0}$ and T–1

(3) ${M}^{0}{L}^{1}{T}^{-1}$ and LT–2

(4) ${M}^{0}{L}^{1}{T}^{-1}$ and T

Concept Questions :-

Dimensions
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Difficulty Level:

From the dimensional consideration, which of the following equation is correct ?

(1) $T=2\pi \sqrt{\frac{{R}^{3}}{GM}}$

(2) $T=2\pi \sqrt{\frac{GM}{{R}^{3}}}$

(3) $T=2\pi \sqrt{\frac{GM}{{R}^{2}}}$

(4) $T=2\pi \sqrt{\frac{{R}^{2}}{GM}}$

High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the relation $v=at+\frac{b}{t+c}$; the dimensions of a, b and c are

(1) $a={L}^{2},\text{\hspace{0.17em}}b=T,\text{\hspace{0.17em}}c=L{T}^{2}$

(2) $a=L{T}^{2},\text{\hspace{0.17em}}b=LT,\text{\hspace{0.17em}}c=L$

(3) $a=L{T}^{-2},b=L,\text{\hspace{0.17em}}c=T$

(4) $a=L,\text{\hspace{0.17em}}b=LT,\text{\hspace{0.17em}}c={T}^{2}$

Concept Questions :-

Dimensions