Two skaters A and B of weights in the ratio 5 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Since there is no external force acting on the system,the center of mass remains stationary. The ratio of the distances moved by the skaters is in

Vedclass · Accepted Answer

$A$ moves $3.5\,m$ and $B$ moves $2.5\,m$

Vedclass · Answer

(D) Since there is no external force acting on the system,the center of mass remains stationary. The ratio of the distances moved by the skaters is inversely proportional to their masses (or weights).Let $m_A$ and $m_B$ be the weights of skaters $A$ and $B$ respectively,where $m_A/m_B = 5/7$.Let $x_A$ and $x_B$ be the distances moved by $A$ and $B$ respectively. Since they meet,$x_A + x_B = 6\,m$.From the conservation of momentum,$m_A x_A = m_B x_B$.Substituting the ratio,$5 x_A = 7 x_B$.Since $x_B = 6 - x_A$,we have $5 x_A = 7(6 - x_A)$.$5 x_A = 42 - 7 x_A \implies 12 x_A = 42 \implies x_A = 3.5\,m$.Then $x_B = 6 - 3.5 = 2.5\,m$.

Two skaters $A$ and $B$ of weights in the ratio $5 : 7$ start facing each other $6\,m$ apart on a horizontal smooth surface. They pull on a rope stretched between them. How far has each moved when they meet?

Similar Questions

$A$ man of $50\, kg$ mass is standing in a gravity-free space at a height of $10\, m$ above the floor. He throws a stone of $0.5\, kg$ mass downwards with a speed of $2\, m/s$. When the stone reaches the floor,the distance of the man above the floor will be ...... $m$.

$A$ system of two particles has masses $m_1$ and $m_2$. If the particle of mass $m_1$ is pushed towards the centre of mass of the particles through a distance $d$,by what distance should the particle of mass $m_2$ be moved to keep the centre of mass of the particles at the original position?

If a bomb is thrown at a certain angle with the horizontal and after exploding on the way the different fragments move in different directions,then the centre of mass

Two masses $m_1$ and $m_2$ start to move towards each other due to mutual gravitational force. If the distance covered by $m_1$ is $x$,then the distance covered by $m_2$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module