A body of mass \(2~\text{kg}\) moving with velocity of \(\vec{v_{in}}=(3\hat{i}+4 \hat{j})~\text{m/s}\) enters into a constant force field of \(6 ~\text N\) directed along positive \(z\text-\)axis. If the body remains in the field for a period of \(\dfrac{5}{3}\) seconds, then velocity of the body when it emerges from force field is:
1. \((4 \hat{\imath}+3 \hat{\jmath}+5 \hat{k})~\text{m/s}\)
2. \((3 \hat{\imath}+4 \hat{\jmath}+5 \hat{k})~\text{m/s}\)
3. \((3 \hat{\imath}+4 \hat{\jmath}-5 \hat{k})~\text{m/s}\)
4. \((3 \hat{\imath}+4 \hat{\jmath}+\sqrt{5} \hat{k} )~\text{m/s}\)
Subtopic:  Newton's Laws |
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An object with mass \(500~\text{g}\) moves along \(x\text-\)axis with speed \(v = 4\sqrt {x} ~\text{m/s.}\) The force acting on the object is:
1. \(4~\text{N}\)
2. \(6~\text{N}\)
3. \(8~\text{N}\)
4. \(5~\text{N}\)
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A player caught a cricket ball of mass \(\mathrm{150 ~g}\) moving at a speed of \(20 \mathrm{~m} / \mathrm{s}.\) If the catching process is completed in \(\mathrm{0.1 ~s ,}\) the magnitude of force exerted by the ball on the hand of the player is:
1. \(\mathrm{150 ~N}\)
2. \(\mathrm{3 ~N}\)
3. \(\mathrm{30~N}\)
4. \(\mathrm{300~N}\)
Subtopic:  Newton's Laws |
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A ball of mass \(120~\text{g}\) moving with initial velocity \(25~\text{m/s}\) is stopped by an external force \({F}\) in \(0.1\) second. Then the value of force is: (in Newton)
1. \(60~\text{N}\)
2. \(40~\text{N}\)
3. \(100~\text{N}\)
4. \(30~\text{N}\)
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A ball released from a height \(10 ~\text{m}\) strikes the ground and rebounds at the height of \(5 ~\text{m}.\) Then the impulse imparted by the ground while collision (given the mass of the ball is \(100~\text g\)) is:
(Take \(g=10~\text{m/s}^2 )\)
1. \((\sqrt2-1)~\text{N-s}\)
2. \((\sqrt2+2)~\text{N-s}\)
3. \((2\sqrt2-1)~\text{N-s } \)
4. \((\sqrt2+1)~\text{N-s } \)
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A block of mass \(20~\text{kg}\) is placed on a rough surface having coefficient of friction \(0.04\) as shown in the figure. Find the acceleration of the system when it is released.
 
1. \(3~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(1~\text{m/s}\)
4. \(4~\text{m/s}\)
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An artillery gun of mass \(M_1\)​ fires a shell of mass \(M_2. \) Assuming no external force acts on the system, what is the ratio of the kinetic energy of the artillery to that of the shell at the instant of firing?
1. \(\dfrac{M_2}{M_1}\) 2. \(\dfrac{M_1+M_2}{M_1}\)
3. \(\dfrac{M_1+M_2}{M_2}\) 4. \(\dfrac{M_1}{M_1+M_2}\)
Subtopic:  Newton's Laws |
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In the system shown below, the pulley for string is ideal. If the acceleration of blocks is \( \frac{g}{8},\) then the ratio of their masses \( \frac{m_1}{m_2}\) is:
   
1. \( \dfrac{9}{7}\)

2. \(\dfrac{8}{7}\)

3. \(\dfrac{5}{7}\)

4. \( \dfrac{9}{8}\)
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The normal force between the table and \(5~\text{kg}\) block as shown in the diagram is:
(take \(g=10~\text{m/s}^2\) )
 
1. \(306 ~\text N\)
2. \(303~\text N\)
3. \(296~\text N\)
4. \(297~\text N\)
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A particle of mass \(500~\text{g}\) is moving with a velocity given by:
\(\vec{v}=(2 t \hat{i}+3 t^2 \hat{j})~ \text{m} / \text{s}.\)
If the force acting on the particle at \(t=1~\text{s}\) is ⁣\(\vec{F}=( \hat{i}+x \hat{j})~ \text{N},\) then the value of \(x\) is:

1. \(6\) 2. \(1\)
3. \(2\) 4. \(3\)
Subtopic:  Newton's Laws |
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