SATHEE: Work Energy and Power - Result Question 48

Work Energy and Power - Result Question 48

51. On a frictionless surface a block of mass $M$ moving at speed $v$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $θ$ to its initial direction and has a speed

$\frac{v}{3}$ . The second block’s speed after the collision is :

[2015 RS]

(a) $\frac{3}{4} v$

(b) $\frac{3}{\sqrt{2}} v$

(d) $\frac{2 \sqrt{2}}{3} v$

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Answer:

Correct Answer: 51. (d)

Solution:

(d) Here, $M_{1} = M_{2}$ and $u_{2} = 0$

$u_{1} = V, V_{1} = \frac{V}{3}; V_{2} = ?$

From figure, along $x$ -axis,

$M_{1} u_{1} + M_{2} u_{2} = M_{1} V_{1} \cos θ + M_{2} V_{2} \cos ϕ \dots$ (i) Along $y$ -axis

$0 = M_{1} V_{1} \sin θ - M_{2} V_{s} \sin ϕ$

By law of conservation of kinetic energy,

$\frac{1}{2} M_{1} u_{1}^{2} + \frac{1}{2} M_{2} u_{2}^{2} = \frac{1}{2} M_{1} V_{1}^{2} + \frac{1}{2} M_{2} V_{2}^{2}$

Putting $M_{1} = M_{2}$ and $u_{2} = 0$ in equation (i), (ii) and (iii) we get,

$θ + ϕ = \frac{π}{2} = 90^{\circ}$

and $u_{1}^{2} = V_{1}^{2} + V_{2}^{2}$

$V^{2} = (\frac{V}{3})^{2} + V_{2}^{2} [∵ u_{1} = V .$ and $. V_{1} = \frac{V}{3}]$

or, $V^{2} - (\frac{V}{3})^{2} = V_{2}^{2}$

$V^{2} - \frac{V^{2}}{9} = V_{2}^{2}$

or $V_{2}^{2} = \frac{8}{9} V^{2} \Rightarrow V_{2} = \frac{2 \sqrt{2}}{3} V$

Work Energy and Power - Result Question 48

51. On a frictionless surface a block of mass $M$ moving at speed $v$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $θ$ to its initial direction and has a speed

Answer:

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Work Energy and Power - Result Question 48

51. On a frictionless surface a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle θ to its initial direction and has a speed

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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51. On a frictionless surface a block of mass $M$ moving at speed $v$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $θ$ to its initial direction and has a speed