Home
Class 11
PHYSICS
A and B are two particles having the sam...

A and B are two particles having the same mass m. A is moving along X-axis with a speed of `10ms^(-1)` and B is at rest. After undergoing a perfectly elastic collision with B, particle A gets scattered through an angle of `30^(@)`. What is th edirection of motion of B, and the speeds of A and B, after the collision?

Text Solution

Verified by Experts

Here, `u=1m//s, theta=30^(@), phi=?, upsilon=?`
As `theta+phi=90^(@) :. =90^(@)-theta=90^(@)-30^(@)=60^(@)`
From `u=upsilon_(1)cos theta+upsilon_(2)cosphi`
`1=upsilon_(1)cos 30^(@)+upsilon_(2)cos 60^(@)=(upsilon_(1)sqrt(3))/(2)+(upsilon_(2))/(2) or upsilon_(1)sqrt(3)+upsilon_(2)=2` ...(i)
Again, as `0=upsilon_(1)sintheta-upsilon_(2)sinphi :. 0=upsilon_(1)sin30^(@)-upsilon_(2)sin60^(@)=(upsilon_(1))/(2)-(upsilon_(2)sqrt(3))/(2)` or `upsilon_(2)=(upsilon_(1))/(sqrt(3))`
Put in (i), `upsilon_(1)sqrt(3)+(upsilon_(1))/(sqrt(3))=2`
`3upsilon_(1)+upsilon_(1)=2sqrt(3)`
`upsilon_(1)=(sqrt(3))/(2)m//s`
Promotional Banner

Topper's Solved these Questions

  • WORK, ENERGY AND POWER

    PRADEEP|Exercise higher order thinking skills|10 Videos

  • WORK, ENERGY AND POWER

    PRADEEP|Exercise value Based Question|5 Videos

  • WORK, ENERGY AND POWER

    PRADEEP|Exercise NCERT EXERCISES WITH SOLUTIONS|30 Videos

  • THERMODYNAMICS

    PRADEEP|Exercise Assertion- Reason Type Questions|19 Videos

Similar Questions

Explore conceptually related problems

Two particles A and B have the same mass m. A is moving along X-axis with a speed of 5 ms^(-1) and B is at rest. After undergoing a perfectly elastic collision with B, particle A gets scat tered through an angle of 60^(@). What is the direction of B, and the speeds of A and B, after the collision ?

Two particles each of mass m moving with equal speed 2m/s along the indicated direction in the figure undergo a perfectly inelastic collision.Velocity of combined system after collision is ?

A and B are two identical balls. A moving with a speed of 6m//s , along the positive X-axis, undergoes a collision with B initially at rest. After collision, each ball moves along directions making angles of +-30^(@) with the X-axis. What are the speeds of A and B after the collision ? I s this collision perfectly eleastic ?

A ball moving with a speed of 10" m s"^(-1) strikes an identical ball such that after the collision the direction of each ball makes an angle 45^(@) with the original line of motion. Find the speeds of the two balls after the collision.

Particle A makes a perfectly elastic collision with anther particle B at rest. They fly apart in opposite direction with equal speeds. If the masses are m_(A)&m_(B) respectively, then

Two particles A and B of mass 3kg and 2kg moving with speed 10m//s and 5m//s as shown in figure. Find the maximum momentum that particle B can have after collision with B .

A ball moving with a speed of 9m//s strikes an identical ball at rest, such that after the collision, the direction of each ball makes an angle of 30^(@) with the original line of motion. Find the speeds of the two balls after collision.

Two particles A and B of mass 3kg and 2kg moving with speed 10m//s and 5m//s as shown in figure. Find the maximum momentum that particles A can have after collision with B .

A ball moving with a speed of 9ms^(-1) strikes an identical ball such that after the collision the direction of each ball makes and angle 30^@ with the original line of motion. Find the speeds of the two balls after the collision.

Knowledge Check

  • A ball moving with a speed of 10" m s"^(-1) strikes an identical ball such that after the collision the direction of each ball makes an angle 45^(@) with the original line of motion. Find the speeds of the two balls after the collision.

    A
    `v_(1)=5sqrt(2)" m"//"s", v_(2)=10sqrt(2)" m"//"s"`
    B
    `v_(1)=10sqrt(2)" m"//"s",v_(2)=10sqrt(2)" m"//"s"`
    C
    `v_(1)=5sqrt(2)" m"//"s",v_(2)=5sqrt(2)" m"//"s"`
    D
    `v_(1)=3sqrt(2)" m"//"s",v_(2)=10sqrt(2)" m"//"s"`

  • Particle A makes a perfectly elastic collision with another particle B at rest. They fly apart in opposite directions with equal speeds. The ratio of their masses m_A//m_B is

    A
    `1/2`
    B
    `1/3`
    C
    `1/4 `
    D
    `1/(sqrt3)`

  • Particle A makes a perfectly elastic collision with anther particle B at rest. They fly apart in opposite direction with equal speeds. If the masses are m_(A)&m_(B) respectively, then

    A
    `2m_(A)=m_(B)`
    B
    `3m_(A)=m_(B)`
    C
    `4m_(A)=m_(B)`
    D
    `sqrt3m_(A)=m_(B)`