Three bricks each of length L and mass M are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is

Question

Three bricks each of length L and mass M are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is (A)  L/4  (B)  L/2  (C)  (3/2)L  (D)  (11/12)L

Tardigrade Admin · Accepted Answer

x1=(L/2) x2=L x3=L+(L/4) x3=(5L/4) ∴ xCM=(m1x1+m2x2+m2x3/3m) =((mL/2)+mL+(m5L/4)/3m) =(11L/12)

Q. Three bricks each of length $L$ and mass $M$ are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is

$L /4$

$L /2$

$(3/2) L$

$(11/12) L$

$(5/6) L$

$x_{1} = \frac{L}{2}$
$x_{2} = L$
$x_{3} = L + \frac{L}{4}$
$x_{3} = \frac{5 L}{4}$
$∴$ $x_{CM} = \frac{m _{1} x _{1} + m _{2} x _{2} + m _{2} x _{3}}{3 m}$
$= \frac{\frac{m L}{2} + m L + \frac{m 5 L}{4}}{3 m}$
$= \frac{11 L}{12}$

Q. Three bricks each of length L and mass M are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is

L/4

L/2

(3/2)L

(11/12)L

(5/6)L

x1​=2L​ x2​=L x3​=L+4L​ x3​=45L​ ∴ xCM​=3mm1​x1​+m2​x2​+m2​x3​​ =3m2mL​+mL+4m5L​​ =1211L​