Can you explain the answer of this question below:Two blocks of the masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block. The velocity of centre of mass isA:10 m/sB:5 m/sC:15 m/sD:20 m/sThe answer is a.

Question

Answer

Answer

Velocity of heavier block (v₂) = 14m/s
Velocity of lighter block (v₁) = 0m/s
Velocity of centre of mass,

Answer

Understanding the Problem
In this scenario, we have two blocks connected by a spring on a frictionless surface. The masses are 10 kg (block A) and 4 kg (block B). When an impulse is applied to block A, it attains a velocity of 14 m/s. We need to determine the velocity of the center of mass (CM) of the entire system.

Velocity of Center of Mass
The velocity of the center of mass (v_cm) can be calculated using the formula:
$$ v_{cm} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} $$
Where:
- $ m_1 $ and $ m_2 $ are the masses of the blocks.
- $ v_1 $ and $ v_2 $ are their respective velocities.

Given Values
- $ m_1 = 10 \, \text{kg} $ (mass of block A)
- $ m_2 = 4 \, \text{kg} $ (mass of block B)
- $ v_1 = 14 \, \text{m/s} $ (velocity of block A)
- $ v_2 = 0 \, \text{m/s} $ (initially at rest)

Calculating the Center of Mass Velocity
Now, substitute the values into the formula:
$$ v_{cm} = \frac{(10 \times 14) + (4 \times 0)}{10 + 4} $$
This simplifies to:
$$ v_{cm} = \frac{140 + 0}{14} = \frac{140}{14} = 10 \, \text{m/s} $$

Conclusion
Thus, the velocity of the center of mass of the system is:
**10 m/s**
Therefore, the correct answer is option **'A'**.

Answer

Kyaa hoga

Answer

(m1v1+m2v2) / m1 +v1

Answer

Why momentum conservation is applicable?

Similar Class 11 Doubts

Two block of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is [IIT(Scr.)-2002]

Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. an external kick gives a velocity of 14 m/s to the heavier block in the direction of lighter one.the velocity gained by the center of mass is?

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