Question

Two particles, of masses M and 2M, moving as shown with speeds of 10 m/s and 5 m/s, collide elastically at the
origin. After the collision, they move along thedirections with speeds v1 and v2, respectively. The value
of v1and v2are nearly:​

Answer 1

Answer:

Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds v1 and v2, respectively. The values of v1 and v2 are nearly : (1)  3.2 m/s and 12.6 m/s (2)  3.2 m/s and 6.3 m/s (3)  6.5 m/s and 6.3 m/s (4)  6.5 m/s and 3.2 m/s

Explanation:

Answer 2

The value of v₁ and v₂ is 6.5 m/s and 6.3 m/s.

Explanation:

Given that,

Mass of first particle = M

Mass of second particle = 2M

Speed of first particle =10 m/s

Speed of second particle = 5 m/s

We need to calculate the velocity

Using conservation of momentum

$m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}$

Put the value into the formula

$M\times10\cos30+2M\times\cos45=2Mv_{1}\cos30+Mv_{2}\cos45$

$5\sqrt{3}+5\sqrt{2}=2v_{1}\dfrac{\sqrt{3}}{2}+\dfrac{v_{2}}{\sqrt{2}}$....(I)

$10\times M\sin30-2M\times5\sin45=Mv_{2}\sin45-2Mv_{1}\sin30$

$5-5\sqrt{2}=\dfrac{v_{2}}{\sqrt{2}}-v_{1}$....(II)

From equation (I) and (II)

We get,

$v_{1}=6.5\ m/s$

$v_{2}=6.3\ m/s$

Hence, The value of v₁ and v₂ is 6.5 m/s and 6.3 m/s.

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Topic : elastic collision

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