Center of mass Quiz 1

Question 1

A rectangular weightless plate is placed on a $$x-y$$ plane having $$4$$ masses at the corner of the rectangle as shown in figure. The coordinates of the center of mass of the system will be $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/167ddfae-cd7b-4597-b607-70adec6ec3d76883886488269367778.png"/>

Accepted Answer

$$\left( 0.3,0.5 \right)$$

Answer

$$\left( 0.5,0.3 \right)$$

Answer

$$\left( 0.2,0.6 \right)$$

Answer

$$\left( 0.6,0.2 \right)$$

Question 2

A bomb disposal team was sent to a station where a suspicious bag had been found in a corner. As they opened the bag, they discovered a ball that split into two pieces weighing $$2\,kg$$ and $$4\,kg$$, with a velocity of $$5\,m/s$$ for the $$2\,kg$$ component. The squad is aware that it was a prank played by a child, so they want to do something productive, so they want to measure the kinetic energy of the greater part of the ball, so that the kinetic energy can be-

Accepted Answer

$$12.5	ext{ }J$$

Answer

$$8.5	ext{ }J$$

Answer

$$4.5	ext{ }J$$

Answer

$$16.5	ext{ }J$$

Question 3

As seen in the diagram, a plate with uniform mass density is mounted on a plane surface with an x-y plane. The system's centre of mass will be placed. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/5d3b72b1-6c3e-4a68-b72a-a33877b421235008701909038434235.png"/>

Accepted Answer

$$\left( 1.5,0.75 \right)$$

Answer

$$\left( 1.5,0.5 \right)$$

Answer

$$\left( 1.5,1.5 \right)$$

Answer

$$\left( 0.5,1.5 \right)$$

Question 4

Ram throws a rock at a velocity of $$5\,ms^{-1}$$ at an angle of $$60^\circ $$ with the horizontal to test his strength, but the stone splits in two parts of $$\dfrac{1}{3}^{rd}$$ and $$\dfrac{2}{3}^{rd}$$ of its original mass at some point during its trajectory.The smaller mass moves along the negative x direction with velocity of $$2	ext{ }m{{s}^{-1}}$$ the velocity of larger part will be-

Accepted Answer

$$4.75	ext{ }m{{s}^{-1}}$$

Answer

$$3.75	ext{ }m{{s}^{-1}}$$

Answer

$$1.25	ext{ }m{{s}^{-1}}$$

Answer

$$5.75	ext{ }m{{s}^{-1}}$$

Question 5

A pulley-ball system is set up by a man who wants to experiment the movement of the centre of mass of the system as shown in figure. If this system is released from rest the acceleration of COM of the system will be $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/2b6d431e-704a-430c-ba05-2bd8520448022459489669613946635.png"/>

Accepted Answer

$$\dfrac{10}{9}\,m/{{s}^{2}}$$

Answer

$$\dfrac{9}{10}\,m/{{s}^{2}}$$

Answer

$$\dfrac{5}{7}\,m/{{s}^{2}}$$

Answer

$$\dfrac{7}{5}\,m/{{s}^{2}}$$