Home
Class 11
PHYSICS
Three interacting particles of masses 10...

Three interacting particles of masses `100g, 200g` and `400g` each hace a velocity of `20 m//s` magnitude along the positive direction of x-axis, y-axis and z-axis. Due to force of interaction the third particle stops moving. The velocity of the second particle is `(10hat(j) + 5hat(k))`. What is the velocity of the first particle ?

A

`20hat(i) + 20hat(j) + 70hat(k)`

B

`10hat(i) + 20hat(j) + 8hat(k)`

C

`30hat(i) + 10hat(j) + 7hat(k)`

D

`15hat(i) + 5hat(j) + 60hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
(A)
Initial momentum `= m_(1) vec(v)_(1) + m_(2)vec(v)_(2) + m_(3)vec(v)_(3) = 2hat(i) + 4hat(j) + 8hat(k)`
When the third particle stops the final momentum `= m_(1)vec(v)_(1) + m_(2)vec(v)_(1) + m_(2)vec(v)_(2) + m_(3)vec(v)_(3) = 0.1vec(v)_(1) + 0.2(10hat(j) + 5hat(k)) + 0`
By principle of conservation of momentum `0.1 vec(v)_(1) + 2hat(j) + hat(k) = 2hat(i) + 4hat(j) + 8hat(k), vec(v)_(1) = 20hat(i) + 20hat(j) + 70hat(k)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CENTRE OF MASS

    ALLEN |Exercise EXERCISE-I|40 Videos

  • CENTRE OF MASS

    ALLEN |Exercise EXERCISE-II|43 Videos

  • BASIC MATHEMATICS USED IN PHYSICS &VECTORS

    ALLEN |Exercise EXERCISE-IV ASSERTION & REASON|11 Videos

  • ELASTICITY, SURFACE TENSION AND FLUID MECHANICS

    ALLEN |Exercise Exercise 5 B (Integer Type Questions)|3 Videos

Similar Questions

Explore conceptually related problems

Find the kinetic energy of a particle of mass 200 g moving with velocity 3hat(i)-5hat(j)+4hat(k) m//s .

A particle is moving with velocity vecv = k( y hat(i) + x hat(j)) , where k is a constant . The genergal equation for its path is

Knowledge Check

  • A particle of mass m and charge q is incident on XZ plane with velocity v in a direction making angle theta with a uniform magnetic field applied along X-axis. The nature of motion performed by the particle is

    A
    Circular
    B
    Helical
    C
    Parabola
    D
    Straight line

    • Similar Questions

    Explore conceptually related problems

    The velocity of a particle moving in the positive direction of the x axis varies as v=5sqrtx , assuming that at the moment t=0 the particle was located at the point x=0 , find acceleration of the particle.

    The velocity of a particle moving with constant acceleration at an instant t_(0) is 10m//s After 5 seconds of that instant the velocity of the particle is 20m/s. The velocity at 3 second before t_(0) is:-

    A particle starts with an initial velocity 2.5 m//s along the posiive x-direction and it accelerates uniformly at the rate 0.50 m//s^2. Find the distance travelled by it in the first two seconds

    V_(x) is the velocity of a particle of a particle moving along the x- axis as shown. If x=2.0m at t=1.0s , what is the position of the particle at t=6.0s ?

    A particle is moving on X- axis. Its velocity time graph is given in the figure. Find distance travelled by the particle in 5 sec .

    A particle of mass 2kg moving with a velocity 5hatim//s collides head-on with another particle of mass 3kg moving with a velocity -2hatim//s . After the collision the first particle has speed of 1.6m//s in negative x-direction, Find (a) velocity of the centre of mass after the collision, (b) velocity of the second particle after the collision. (c) coefficient of restitution.

    Two balls of masses 100 g and 200g are moving along the same line and direction with velocities 1ms^(-1) and 2 ms^(-1) respectively. They collide and after the collision, the first ball moves at a velocity of 2ms^(-1) Determine the velocity of the second ball.

    Home
    Profile