Question

A particle of mass 1 kg has potential energy, P.E, = 3x + 4y. At t = 0, the particle is at rest at (6, 4). Work done by external force to displace the particle from rest to the point of crossing the x axis is

• A. 25 J
• B. 20 J
• C. 15 J
• D. 52 J

Answer 1

Answer: (A)

25 J

Answer 2

The particle was initially at rest at (6, 4)

∴ x = 6 + $\frac { 1 } { 2 }$ a_xt²

and y = 4 + $\frac { 1 } { 2 }$ a_yt² ………….. (i)

Acceleration

i.e.,

a = (3² + 4²)^1/2 = 5 ms^-2 ………… (ii)

Substituting the value of a from (ii) in (i)

x = $\left( 6 - \frac { 3 } { 2 } t ^ { 2 } \right)$

and y = (4 – 2t²)

Now y = 0 when particle crosses x – axis

∴ t =

Displacement S = $\frac { 1 } { 2 }$ at²

= $\frac { 1 } { 2 } \times 5 \times 2$ = 5m

Then work done = F.S. = 5 × 5 = 25 J