Question

A body of mass 2M in motion undergoes a one-dimensional semi-elastic collision with a stationary body of mass 3M. If the final K.E. of the system is 7/16 times the initial K.E. of the system then 1/e is equal to : (e is the coefficient of restitution)
1) 4 2) 6 3) 3 4) 2

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Answer 1

The value of 1/e is equal to 1) 4.

Given,

Mass of the body in motion= 2M

Mass of the stationary body= 3M

Final K.E = $\frac{7}{16}$ times the initial K.E

To Find,

$\frac{1}{e}$ value (where e is the coefficient of restitution)

Solution,

Let mass of the moving body be M1= 2M and its initial velocity u1 be 'u'.

Let the mass of the stationary body be M2- 3M and its velocity u2= 0.

Therefore, $KE_{f} =\frac{7}{16} KE_{i}$

Now, we know Δ$KE=KE_{i} -KE_{f}$

⇒$KE_{i} - \frac{7}{16} KE_{i}$

⇒ $\frac{9}{16}KE_{i}$

⇒ $\frac{9}{16} * \frac{1}{2} (2M)u^{2}$

which gives, ΔKE= $\frac{9}{16} Mu^{2}$  - (1)

Now, we know, Δ$KE= \frac{1}{2} \frac{m1m2}{m1+m2} (u1-u2)^{2} (1-e^{2} )$

Which gives, Δ$KE=\frac{3M}{5} u^{2} (1-e^{2} )$   - (2)

By using Equations (1) and (2),

$\frac{9}{16} Mu^{2} = \frac{3}{5} Mu^{2} (1-e^{2} )$

⇒$\frac{5}{16} = 1 - e^{2}$

⇒$e = \sqrt{\frac{1}{16} }$

⇒$e =\frac{1}{4}$

⇒$\frac{1}{e} = 4$

Therefore, considering e as the coefficient of restitution, the value of 1/e is option 1) 4.

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Answer 2

Answer:

4 is the answer

OPTION 1

Explanation:

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