The velocity v in cm - s of a particle is given in terms of time t by the equation- v - at - b - t - c- Dimensions of a- b and c areA- A - L 2- B - T - C - LT 2B- A - LT -2- B - LT - C - LC- A - LT -2- B - L - C - TD- A - L - B - LT - C - T 2

The correct option is C A LT^ 2, B L, C T v = at + b/t+c [ at ]= [ v ] [ LT^ 1 ] [ a ]= [ LT^ 1 ]/T = [ LT^ 2 ] Dimensions of c = [ c ] = [T] (We can ...

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Standard XII

Physics

Vector Addition

The velocity ...

Question

The velocity $υ$ (in cm/s) of a particle is given in terms of time (t) by the equation: $υ = a t + \frac{b}{t + c} .$ Dimensions of a, b and c are

$A - L^{2}, B - T, C - L T^{2}$

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$A - L T^{- 2}, B - L T, C - L$

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$A - L T^{- 2}, B - L, C - T$

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$A - L, B - L T, C - T^{2}$

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Solution

The correct option is C
$A - L T^{- 2}, B - L, C - T$

$v = a t + \frac{b}{t + c} [a t] = [v] [L T^{- 1}] [a] = \frac{[L T^{- 1}]}{T} = [L T^{- 2}] Dimensions of c = [c] = [T] (We can add quantities of same dimensions only.) [\frac{b}{t + c}] = [v] = [L T^{- 1}] [b] = [L T^{- 1}] [T] = [L]$

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The velocity υ (in cm/s) of a particle is given in terms of time (t) by the equation: υ=at+bt+c. Dimensions of a, b and c are

The correct option is C A−LT−2,B−L,C−T v=at+bt+c[at]=[v][LT−1][a]=[LT−1]T=[LT−2]Dimensions ofc=[c]=[T](We can add quantities of same dimensions only.)[bt+c]=[v]=[LT−1][b]=[LT−1][T]=[L]

The velocity $υ$ (in cm/s) of a particle is given in terms of time (t) by the equation: $υ = a t + \frac{b}{t + c} .$ Dimensions of a, b and c are

The correct option is C
$A - L T^{- 2}, B - L, C - T$

$v = a t + \frac{b}{t + c} [a t] = [v] [L T^{- 1}] [a] = \frac{[L T^{- 1}]}{T} = [L T^{- 2}] Dimensions of c = [c] = [T] (We can add quantities of same dimensions only.) [\frac{b}{t + c}] = [v] = [L T^{- 1}] [b] = [L T^{- 1}] [T] = [L]$