Question:
A block of mass $M$ moves with a velocity $v$ along a frictionless horizontal surface towards another block of mass $2M$ at rest. The velocity of the center of mass of the system of blocks is
A block of mass $M$ moves with a velocity $v$ along a frictionless horizontal surface towards another block of mass $2M$ at rest. The velocity of the center of mass of the system of blocks is
Show Hint
The center of mass velocity is the weighted average of the velocities of individual masses.
Updated On: Apr 7, 2026
- $\frac{v}{2}$
- $2v$
- $3v$
- $\frac{v}{3}$
$\frac{v}{4}$
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: The velocity of the center of mass is given by: \[ V_{{cm}} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \] where $m_1 = M$, $v_1 = v$, $m_2 = 2M$, and $v_2 = 0$.
Step 2: Substituting the values: \[ V_{{cm}} = \frac{M v + 2M \times 0}{M + 2M} \] \[ V_{{cm}} = \frac{M v}{3M} = \frac{v}{3} \]
Step 3: Therefore, the correct answer is (D).
Was this answer helpful?
1
0
Top KEAM Physics Questions
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- Two capillary tubes A and B of diameter $1\, mm$ and $2\, mm$ respectively are dipped vertically in a liquid. If the capillary rise in A is 6 cm, then the capillary rise in B is
- In the circuit given in figure, 1 and 2 are ammeters. Just after key K is pressed to complete the circuit, the reading will be
- A plate has a length $ 5\pm 0.1\text{ }cm $ and breadth $ 2\pm 0.01\text{ }cm $ . Then the area of the plate is:
View More Questions
Top KEAM Center of Mass Questions
- The X and Y coordinates of the three particles of masses m, 2m and 3m are respectively (0,0), (1,0) and (-2,0). The X-coordinate of the centre of mass of the system is
- 4 masses are placed at 4 corners of square ABCD. If one mass is removed from the corner B, then the centre of mass lies in the line joining
- The center of mass of a rod of length \( l \) is at a distance ______ from one end of the rod.
- Two bodies A and B of masses 80 g and 120 g move with same speed, $6~cm~s^{-1}$ in a plane. The speed of the centre of mass of the system is
- The objects and the corresponding positions of centre of mass are given below. The FALSE one is
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions