Question

a body moving 2kg initially moving with a velocity of 2m/s, collides with another body of mass 10kg at rest. after collision the velocity of the first object becomes 1m/s. find the velocity.​

for class 9th please solve this question please help me it is urgent needed

Answer 1

Answer:

• Velocity of body of mass 10 kg after collision = 0.6 m/s or 0.2 m/s

Depending on the direction in which first body will move after collision.

Explanation:

Given

• Mass of first body, m = 2 kg
• Mass of second body, M = 10 kg

• Initial velocity of first body, u = 2m/s
• Initial velocity of second body, U = 0 m/s

• Final velocity of first body, v = -1 m/s

[ when first body will move in the opposite direction after collision]

and,

• Final velocity of first body, v' = 1 m/s

[ when first body will move in the same initial direction after collision]

To find

• Final velocity of second body, V =?

Knowledge required

• Law of conservation of linear momentum

According to law of conservation of linear momentum the total momentum of system before collision is equal to the total momentum of system after collision.

For two bodies of masses m and M, initial velocities u and U, final velocities v and V respectively, by law of conservation of momentum

→ m u + M U = m v + M V

Solution

Using law of conservation of linear momentum

Considering the case when first body will move in opposite direction after collision:

→ m u + M U = m v + M V

putting corresponding values

→ 2 × 2 + 10 × 0 = 2 × (-1) + 10 × V

→ 4 + 0 = -2 + 10 V

→ 4 + 2 = 10 V

→ 6 = 10 V

→ V = 0.6 m/s

and,

Considering the case when first body will move in same initial direction after collision:

→ m u + M V = m v' + M V

putting corresponding values

→ 2 × 2 + 10 × 0 = 2 × 1 + 10 × V

→ 4 + 0 = 2 + 10 V

→ 4 - 2 = 10 V

→ 2 = 10 V

→ V = 0.2 m/s

Therefore,

• Velocity of the second body of mass 10 kg after collision would be 0.6 m/s. (when first body will move opposite to direction of initial motion after colliding.)

and

• Velocity of second body of mass 10 kg after collision would be 0.2 m/s. (when first body will move in same initial direction of it's motion after colliding.)

Answer 2

Given:

A body moving 2kg initially moving with a velocity of 2m/s, collides with another body of mass 10kg at rest. after collision the velocity of the first object becomes 1m/s.

To find:

The velocity of 10 kg object ?

Concept:

In this type of questions, it is best to apply the principle of "CONSERVATION OF LINEAR MOMENTUM" since no external force is involved.

According to this principle, the initial and final momentum for both the bodies will be equal.

$\boxed{ \bold{(m1)(u1) + (m2)(u2) = (m1)(v1) + (m2)(v2)}}$

Calculation:

Case 1: (When the final velocity of 2kg object is 1 m/s in the initial direction after collision)

$\rm \therefore \: (m1)(u1) + (m2)(u2) = (m1)(v1) + (m2)(v2)$

$\rm = > \: (2)(2) + (10)(0) = (2)(1) + (10)(v2)$

$\rm = > \: 4 + 0= 2 + (10)(v2)$

$\rm = > \: (10)(v2) = 2$

$\rm = > \: v2 = 0.2 \: m {s}^{ - 1}$

Case 2: (When the final velocity of 1 kg mass become 1 m/s but in the opposite direction after collision):

$\rm \therefore \: (m1)(u1) + (m2)(u2) = (m1)(v1) + (m2)(v2)$

$\rm = > \: (2)(2) + (10)(0) = (2)( - 1) + (10)(v2)$

$\rm = > \: 4 + 0 = - 2 + (10)(v2)$

$\rm = > \: (10)(v2) = 6$

$\rm = > \: v2 = 0.6 \: m {s}^{ - 1}$

So, final velocity of 10 kg block can be 0.2 m/s or 0.6 m/s depending upon the corresponding case.

Hope It Helps.