Q. No.A ball is traveling with uniform translatory motion. This means that:
| 1. | it is at rest. |
| 2. | the path can be a straight line or circular and the ball travels with uniform speed. |
| 3. | all parts of the ball have the same velocity (magnitude and direction) and the velocity is constant. |
| 4. | the center of the ball moves with constant velocity and the ball spins about its center uniformly. |
A cricket ball of mass 150 g has an initial velocity \(\small {u = \left(3 \hat{i} + 4 \hat{j} \right) \text {ms}^{- 1}}\) and a final velocity \(\small {v = - \left( 3 \hat{i} + 4 \hat{j} \right) \text{ms}^{- 1}}\), after being hit. The change in momentum (final momentum-initial momentum) is (in kgm/s)
1. \(\text {zero}\)
2. \(-\left ( 0.45\hat{i}+0.6\hat{j} \right ) \)
3. \(-\left ( 0.9\hat{i}+1.2\hat{j} \right ) \)
4. \(-5\left ( \hat{i} +\hat{j}\right ) \)
A cricket ball of mass 150 g has an initial velocity \(\small {u = \left(3 \hat{i} + 4 \hat{j} \right) \text {ms}^{- 1}}\) and a final velocity \(\small {v = - \left( 3 \hat{i} + 4 \hat{j} \right) \text{ms}^{- 1}}\), after being hit, the magnitude of the momentum transferred during the hit is:
1. zero
2. 0.75 kg-ms–1
3. 1.5 kg-ms–1
4. 14 kg-ms–1
Conservation of momentum in a collision between particles can be understood from:
| 1. | conservation of energy |
| 2. | newton's first law only |
| 3. | newton's second law only |
| 4. | both Newton's second and third law |
A hockey player is moving northward and suddenly turns westward at the same speed to avoid an opponent. The force that acts on the player is:
| 1. | frictional force along westward |
| 2. | muscle force along southward |
| 3. | frictional force along south-West |
| 4. | muscle force a south-West |
A body of mass \(2~\text{kg}\) travels according to the law \(x \left( t \right) = pt + qt^2+ rt^3\) where,\(\) \(p = 3 ~\text{ms }^{−1 },\) \(q = 4 ~\text{ms }^{−2}\) and \(r = 5 ~\text{ms }^{−3}\). The force acting on the body at \(t = 2 ~\text{s }\) is
1. \(136~\text{N}\)2. \(134~\text{N}\)
3. \(158~\text{N}\)
4. \(68~\text{N}\)
A body with a mass of \(5\) kg is acted upon by a force \(\vec{F}=( -3\hat{i} +4\hat{j})\) N. If its initial velocity at \(t=0\) is \(\vec{v}= ( 6\hat{i} -12\hat{j} )\) m/s, the time at which it will just have a velocity along the Y-axis is:
1. never
2. \(10\) s
3. \(2\) s
4. \(15\) s
A car of mass \(m\) starts from rest and acquires a velocity along the east, \(v=v\mathrm{\hat{i}}(v>0)\) in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is:
| 1. | \(mv/2 \) eastward and is exerted by the car engine. |
| 2. | \(mv/2\) eastward and is due to the friction on the tires exerted by the road. |
| 3. | more than \(mv/2\) eastward exerted due to the engine and overcomes the friction of the road. |
| 4. | \(mv/2\) exerted by the engine. |
The motion of a particle of mass \(m\) is given by \(x=0\) for \(t<0 ~\text s\), \(x(t)=A~\text {sin}~4\pi t\) for \(0<t<(1/4) \text s ~(A>0)\), and \(x=0\) for \(t>(1/4) ~\text s\). Then:
| (a) | The force at \(t=(1/8) ~\text s \) on the particle is \(-16 \pi^2\text{Am}\) |
| (b) | The particle is acted upon by an impulse of magnitude \(4 \pi^2 \text{Am}\) at \(t=0 ~\text s\) and \(t=(1/4) ~\text s\) |
| (c) | The particle is not acted upon by any force |
| (d) | The particle is not acted upon by a constant force |
| (e) | There is no impulse acting on the particle |
Which of the following statement/s is/are true?
| 1. | (a, c, d, e) | 2. | (a, c) |
| 3. | (b, c, d) | 4. | (a, b, d) |
In the figure, the coefficient of friction between the floor and body \(B\) is \(0.1.\) The coefficient of friction between bodies \(B\) and \(A\) is \(0.2.\) A force \(F\) is applied as shown on \(B.\) The mass of \(A\) is \(m/2\) and of \(B\) is \(m.\)
| (a) | The bodies will move together if \(F = 0.25\text{mg}\) |
| (b) | The \(A\) will slip with \(B\) if \(F = 0.5\text{mg}\) |
| (c) | The bodies will move together if \(F = 0.5\text{mg}\) |
| (d) | The bodies will be at rest if \(F = 0.1\text{mg}\) |
| (e) | The maximum value of \(F\) for which the two bodies will move together is \(0.45\text{mg}\) |
Which of the following statement(s) is/are true?
1. (a), (b), (d), (e)
2. (a), (c), (d), (e)
3. (b), (c), (d)
4. (a), (b), (c)
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