Question

A car of mass 1500 kg moving at a speed of 90 $km{h}^{-1}$ collides with another car at rest. After the collision, both have a common velocity of 50$km{h}^{-1}$ . The mass of the car which is initially at rest is _____ kg.

• A. 1100
• B. 1200
• C. 1300
• D. 1400

Answer 1

The correct option is B

1200

The explanation for the correct answer

Step 1: Given Data

1. The mass$\left(m_1\right)$ of a car is$1500kg$.
2. The car is moving at a speed$\left(v_1\right)$$90km/h=90\times \frac{5}{18}m/s=25m/s$.
3. The car collides with another car that was initially at rest($v_2=0$).
4. After the collision, both the cars move at a common speed$\left(V\right)$ which is equal to$50km/h=50\times \frac{5}{18}m/s=\frac{250}{18}m/s$.

Step 2: Calculation of the mass of the second car

Here$m_1=massoffirstcar$, $v_1=velocityofthefirstcar$

$m_2=massofthesecondcar$, $v_2=velocityofthesecondcar$

Applying the law of conservation of momentum we can get

$m_1{v}_1+m_2{v}_2=\left(m_1+m_2\right)V$

$\Rightarrow 1500\times 25+m_2\times 0=\left(m_1+m_2\right)\times \frac{250}{18}$

$\Rightarrow \left(1500+m_2\right)=1500\times 25\times \frac{18}{250}=150\times 18$

$\Rightarrow \left(1500+m_2\right)=2700$

$\Rightarrow m_2=2700-1500=1200kg$

Hence, the correct answer is (B).