Questions & Answers of Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

Question No. 116

GATE - 2016
01

A point mass having mass M is moving with a velocity V at an angle $\theta$to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is

(A) $-2MV\;\cos\;\theta\;\widehat j$
(B) $2MV\;\sin\;\theta\;\widehat j$
(C) $2MV\;\cos\;\theta\;\widehat j$
(D) $-2MV\;\sin\;\theta\;\widehat j$

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(D) $-2MV\;\sin\;\theta\;\widehat j$

Subject : Engineering Mechanics

Topic : Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

Question No. 140

GATE - 2016
02

A mass of 2000 kg is currently being lowered at a velocity of 2 m/s from the drum as shown in the figure. The mass moment of inertia of the drum is $150\mathrm{kg}-\mathrm m^2$. On applying the brake, the mass is brought to rest in a distance of 0.5 m. The energy absorbed by the brake (in kJ) is __________

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14.1 : 14.3

Subject : Engineering Mechanics

Topic : Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

Question No. 50

GATE - 2015
02

A ball of mass 0.1 kg, initially at rest, is dropped from height of 1 m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20% . The height (in m) to which the ball will rise is _____.

Show Answer

0.64

Subject : Engineering Mechanics

Topic : Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

Explanation :

. during impact $m_1v_1$ = $m_2v_2$

but here $m_1$ = $m_2$ $\therefore$ $v_1$ = $v_2$

Now v = $\begin{array}{l}\sqrt{2gh}\\\end{array}$ also $v_1$ = 0.8 $v_1$

$\begin{array}{l}h=\frac{v^2}{2g}\\\end{array}$

$h_1$ = $\begin{array}{l}v_1^2/2g\\\end{array}$ $h_2$ = $\begin{array}{l}v_2^2/2g\\\end{array}$

= $(0.8 v_1)^2/2g$

= 0.64 $(v_1^2/2g)$

= 0.64 $h_1$

= 0.64 x 1

= 0.64 m .

Question No. 116

GATE - 2015
01

A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be____.

Show Answer

7.8 to 8.2

Subject : Engineering Mechanics

Topic : Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

Explanation :

For elastic collision

$m_1u_1+m_2u_2=m_1v_1+m_2v_2\;\;\_\_(1)moment\;conservation$

$(1\times12)+(2\times0)=(1\cdot v_1)+(2\cdot v_2)$

$12+0=v_1+2v_2\;\;\_\_(2)$

$1/2\;m_1u_1^2+1/2\;m_2u_2^2=1/2\;m_1v_1^2+1/2\;m_2v_2^2\;\_\_(3)$

$(1/2\cdot1\cdot12^2)+(1/2\cdot2\cdot0^2)=(1/2\cdot1\cdot v_1^2)+(1/2\cdot2\cdot v_2^2)$

$144+0=v_1^2+2v_2^2\;\;\_\_(4)$

$From\;(2)\;\;v_1=12-2v_2$

$144=(12-2v_2)^2+2v_2^2$

$144=144-48v_2+4v_2+2v_2^2$

$6v_2^2-48v_2=0$

$6v_2(v_2-8)=0$

$\therefore\;v_2=8\;m/sec$

Question No. 219

GATE - 2014
01

A mass m₁ of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m₂ of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is

(A) 0.6
(B) 0.1
(C) 0.01
(D) 0

Show Answer

(D) 0

Subject : Engineering Mechanics

Topic : Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

Question No. 22

GATE - 2011
01

The coefficient of restitution of a perfectly plastic impact is

(A) 0
(B) 1
(C) 2
(D) ∞

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(A) 0

Subject : Engineering Mechanics

Topic : Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

Question No. 32

GATE - 2011
02

A stone with mass of 0.1 kg is catapulted as shown in the figure. The total force F_x (in N) exerted by the rubber band as a function of distance x (in m) is given by F_x = 300x². If the stone is displaced by 0.1m from the un-stretched position (x = 0) of the rubber band, the energy stored in the rubber band is

(A) 0.01 J
(B) 0.1 J
(C) 1 J
(D) 10 J

Show Answer

(B) 0.1 J

Subject : Engineering Mechanics

Topic : Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

Question No. 12

GATE - 2007
01

During inelastic collision of two particles, which one of the following is conserved?

(A) total linear momentum only
(B) total kinetic energy only
(C) both linear momentum and kinetic energy
(D) neither linear momentum nor kinetic energy

Show Answer

(A) total linear momentum only

Subject : Engineering Mechanics

Topic : Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

Questions & Answers of Impulse and Momentum (Linear and Angular) and Energy Formulations, Collisions

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(D) $-2MV\;\sin\;\theta\;\widehat j$

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14.1 : 14.3

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0.64

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7.8 to 8.2

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(D) 0

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(A) 0

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(B) 0.1 J

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(A) total linear momentum only

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