A stone of mass 500 g is dropped from the top of a tower of 100 m height. Simultaneously another stone of mass 1 kg is thrown horizontally with a speed of 10 m s- 1 from same point. The height of the centre of mass of the above two stone system after 3 sec is (g = 10 m s- 2)

Question

A stone of mass 500 g is dropped from the top of a tower of 100 m height. Simultaneously another stone of mass 1 kg is thrown horizontally with a speed of 10 m s- 1 from same point. The height of the centre of mass of the above two stone system after 3 sec is (g = 10 m s- 2) (A) 45 m (B) 35 m (C) 55 m (D) none of these

Tardigrade Admin · Accepted Answer

If height of stones is h1 and h2 after t=3 sec then, h1=100-(1/2)gt2=55 m h2=100-(1/2)gt2=55 m ∴ height of centre of mass of the two stone system, hC M=(m1 h1 + m2 h2/m1 + m2)=55 m

Q. A stone of mass $500 g$ is dropped from the top of a tower of $100 m$ height. Simultaneously another stone of mass $1 k g$ is thrown horizontally with a speed of $10 m s^{- 1}$ from same point. The height of the centre of mass of the above two stone system after $3 sec$ is $(g = 10 m s^{- 2})$

$45 m$

$35 m$

$55 m$

none of these

If height of stones is $h_{1}$ and $h_{2}$ after $t = 3 sec$ then,
$h_{1} = 100 - \frac{1}{2} g t^{2} = 55 m$
$h_{2} = 100 - \frac{1}{2} g t^{2} = 55 m$
$∴$ height of centre of mass of the two stone system,
$h_{CM} = \frac{m _{1} h _{1} + m _{2} h _{2}}{m _{1} + m _{2}} = 55 m$

Q. A stone of mass 500g is dropped from the top of a tower of 100m height. Simultaneously another stone of mass 1kg is thrown horizontally with a speed of 10ms−1 from same point. The height of the centre of mass of the above two stone system after 3sec is (g=10ms−2)

45m

35m

55m