A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is 3M , the distance that the man moves relative to the ground is

Question

A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is 3M , the distance that the man moves relative to the ground is (A) (L/4) (B) (3 L/4) (C) (2 L/3) (D) (L/3)

Tardigrade Admin · Accepted Answer

3mx=m(L - x), ⇒ 4mx=3L ⇒ x=(L/4) ∴ displacement of man =L-x=L-(L/4)=(3 L/4)

Q. A man of mass $M$ stands at one end of a plank of length $L$ which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is $3 M$ , the distance that the man moves relative to the ground is

$\frac{L}{4}$

$\frac{3 L}{4}$

$\frac{2 L}{3}$

$\frac{L}{3}$

$3 m x = m (L - x),$
$\Rightarrow 4 m x = 3 L$
$\Rightarrow x = \frac{L}{4}$
$∴$ displacement of man $= L - x = L - \frac{L}{4} = \frac{3 L}{4}$

Q. A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is 3M , the distance that the man moves relative to the ground is

4L​

43L​

32L​

3L​