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 other end of the plank. If the mass of the plank is ( M /3), then the distance that the man moves relative to 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 other end of the plank. If the mass of the plank is ( M /3), then the distance that the man moves relative to ground is : (A) (3 L /4) (B) ( L /4) (C) (4 L /5) (D) ( L /3)

Tardigrade Admin · Accepted Answer

Le the distance moved by plank is x m 1 Δ x 1+ m 2 Δ x 2=0 M ( L - x )+( M /3)(- x )=0 ⇒ x =(3 L /4) ∴ distance moved by person w.r.t. to ground = L - x =( 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 other end of the plank. If the mass of the plank is $\frac{M}{3}$ , then the distance that the man moves relative to ground is :

$\frac{3 L}{4}$

$\frac{L}{4}$

$\frac{4 L}{5}$

$\frac{L}{3}$

Le the distance moved by plank is $x$
$m_{1} Δ x_{1} + m_{2} Δ x_{2} = 0$
$M (L - x) + \frac{M}{3} (- x) = 0$
$\Rightarrow x = \frac{3 L}{4}$
$∴$ distance moved by person w.r.t. to ground
$= L - x = \frac{L}{4}$

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 other end of the plank. If the mass of the plank is 3M​, then the distance that the man moves relative to ground is :

43L​

4L​

54L​

3L​