A stationary pulley carries a rope one end of which supports a ladder with a man and the other a counterweight of mass M . The man of mass m climbs up a distance l with respect to the ladder and then stops. The displacement of the centre of mass of this system is

Question

A stationary pulley carries a rope one end of which supports a ladder with a man and the other a counterweight of mass M . The man of mass m climbs up a distance l with respect to the ladder and then stops. The displacement of the centre of mass of this system is (A) (m l/M + m) (B) (m l/2 M) (C) (m l/M + 2 m) (D) (m l/2 M + m)

Tardigrade Admin · Accepted Answer

From the question mass of the ladder is

(M - m)

.
Let's assume that counterweight goes up by distance

x

then ladder also goes down by

x

. Therefore from the ground frame, man goes up by

(l - x)

.

Then distance moved by the center of mass is given by,

x_{c m} = \frac{M ( x ) + m ( l - x ) + ( M - m ) ( - x )}{2 M}

x_{c m} = \frac{m l}{2 M}

Q. A stationary pulley carries a rope one end of which supports a ladder with a man and the other a counterweight of mass $M$ . The man of mass $m$ climbs up a distance $l$ with respect to the ladder and then stops. The displacement of the centre of mass of this system is

$\frac{m l}{M + m}$

$\frac{m l}{2 M}$

$\frac{m l}{M + 2 m}$

$\frac{m l}{2 M + m}$

Q. A stationary pulley carries a rope one end of which supports a ladder with a man and the other a counterweight of mass M . The man of mass m climbs up a distance l with respect to the ladder and then stops. The displacement of the centre of mass of this system is

M+mml​

2Mml​

M+2mml​

2M+mml​

Q. A stationary pulley carries a rope one end of which supports a ladder with a man and the other a counterweight of mass $M$ . The man of mass $m$ climbs up a distance $l$ with respect to the ladder and then stops. The displacement of the centre of mass of this system is

$\frac{m l}{M + m}$

$\frac{m l}{2 M}$

$\frac{m l}{M + 2 m}$

$\frac{m l}{2 M + m}$