Three masses are placed on the x-axis: 300 g at origin, 500 g at x=40 cm and 400 g at x=70 cm. The distance of the centre of mass from the origin is

  • Option 1)

    40 cm

  • Option 2)

    45 cm

  • Option 3)

    50 cm

  • Option 4)

    30 cm

 

Answers (1)
P Prateek Shrivastava

As learnt in

Centre of mass when some mass is added in the body -

{vec{r}_{CM}}=frac{m_{1}vec{r_{1}}+{m_{2}}vec{r}_{2}}{m_{1}+m_{2}}

- wherein

m1 &  vec{r_{1}} are mass and position of centre of mass for whole body. m2 & vec{r_{2}} are mass and position of centre of mass of added mass.

 

 X_{c}=\frac{m_{1}x_{1}+m_{2}x_{2}+m_{3}x_{3}}{m_{1}+m_{2}+m_{3}}

X_{c}=\frac{300 \times (0)+500 \times 40 + 400 \times 70}{300+500+400}

X_{c}=\frac{120}{3}=40 cm


Option 1)

40 cm

This option is correct.

Option 2)

45 cm

This option is incorrect.

Option 3)

50 cm

This option is incorrect.

Option 4)

30 cm

This option is incorrect.

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