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Standard XII

Physics

Limitation of Dimensional Analysis

The potential...

Question

The potential energy of a particle of mass 5 kg moving in x-y plane is given by equation, $U = - 7 x + 24 y$ Joule.Here x and y are in meter at t=0,the particle is at origin and moving with velocity $(2^i + 3^j)$ m/s.The magnitude of acceleration of particle is

3 m / s^{2}

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5 m / s^{2}

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31 m / s^{2}

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15 m / s^{2}

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Solution

The correct option is B $5 m / s^{2}$
$m = 5 k g$
$u = - 7 x + 24 y$
$\to v = 2^i + 3^j F_{x} = - \frac{d u}{d x} = 7 F_{y} = \frac{d u}{d y} = - 24 ∣ ∣ ∣ \to F ∣ ∣ ∣ = \sqrt{49 + 576} = 25 a = \frac{F}{m} = \frac{25}{5} = 5 \frac{m}{s^{2}}$

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The potential energy of a particle of mass 5 kg moving in x-y plane is given by equation,U=−7x+24y Joule.Here x and y are in meter at t=0,the particle is at origin and moving with velocity (2^i+3^j) m/s.The magnitude of acceleration of particle is

The correct option is B 5m/s2m=5kgu=−7x+24y→v=2^i+3^jFx=−dudx=7Fy=dudy=−24∣∣∣→F∣∣∣=√49+576=25a=Fm=255=5ms2

The potential energy of a particle of mass 5 kg moving in x-y plane is given by equation, $U = - 7 x + 24 y$ Joule.Here x and y are in meter at t=0,the particle is at origin and moving with velocity $(2^i + 3^j)$ m/s.The magnitude of acceleration of particle is

The correct option is B $5 m / s^{2}$
$m = 5 k g$
$u = - 7 x + 24 y$
$\to v = 2^i + 3^j F_{x} = - \frac{d u}{d x} = 7 F_{y} = \frac{d u}{d y} = - 24 ∣ ∣ ∣ \to F ∣ ∣ ∣ = \sqrt{49 + 576} = 25 a = \frac{F}{m} = \frac{25}{5} = 5 \frac{m}{s^{2}}$