For better understanding 11th ki physics chapter motion in one two and three dimensional study carefully

Introduction:
In this scenario, a 10 gram bullet with a velocity of 500 meters per second collides with a stationary piece of ice with a mass of 10 kg on a frictionless plane. We need to determine the velocity of the ice after the collision.

Understanding the problem:
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces act on the system.

Solution:
Step 1: Convert the mass of the bullet to kg:
The mass of the bullet is given as 10 grams. To convert it to kilograms, we divide it by 1000.
Mass of the bullet = 10 grams ÷ 1000 = 0.01 kg

Step 2: Calculate the initial momentum:
The initial momentum of the system is given by the product of the mass and velocity of the bullet.
Initial momentum = Mass of the bullet × Velocity of the bullet
Initial momentum = 0.01 kg × 500 m/s = 5 kg·m/s

Step 3: Apply the principle of conservation of momentum:
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Total momentum before collision = Total momentum after collision

Step 4: Calculate the final momentum:
Since the ice is initially stationary, its initial momentum is zero.
Total momentum before collision = Momentum of the bullet
Total momentum after collision = Momentum of the ice

Step 5: Calculate the velocity of the ice:
Using the equation for momentum, we can rearrange it to solve for the velocity of the ice:
Momentum = Mass × Velocity
Velocity = Momentum / Mass

Since the total momentum after the collision is zero (as the ice comes to rest), the velocity of the ice will also be zero.

Conclusion:
After the collision, the piece of ice will be at rest on the frictionless plane, resulting in a velocity of zero meters per second.