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. |
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)
Mass \(m_{1}\) moves on a slope making an angle \(\theta\) with the horizontal and is attached to mass \(m_{2}\) by a string passing over a frictionless pulley as shown in the figure. The coefficient of friction between \(m_{1}\) and the sloping surface is \(\mu\).
| (a) | If \(m_{2} > m_{1} \text{sin} \theta \), the body will move up the plane. |
| (b) | If \(m_{2} > m_{1} (\text{sin} \theta +\mu \text{cos} \theta)\), the body will move up the plane. |
| (c) | If \(m_{2} < m_{1} (\text{sin} \theta +\mu \text{cos} \theta)\), the body will move up the plane. |
| (d) | If \(m_{2} < m_{1} (\text{sin} \theta -\mu \text{cos} \theta)\), the body will move down the plane. |
| 1. | (a), (d) | 2. | (a), (c) |
| 3. | (c), (d) | 4. | (b), (d) |
In figure a body \(A\) of mass \(m\) slides on a plane inclined at angle \(\left(\theta_{1}\right)\) to the horizontal and \(\mu\) is the coefficient of friction between \(A\) and the plane. \(A\) is connected by a light string passing over a frictionless pulley to another body \(B,\) also of mass \(m\), sliding on a frictionless plane inclined at an angle \(\left(\theta_{2}\right)\) to the horizontal.
| (a) | A will never move up the plane |
| (b) | A will just start moving up the plane when \(\mu = \dfrac{{\sin} \left(\theta\right)_{2} - {\sin} \left(\theta\right)_{1}}{{\cos} \left(\theta\right)_{1}}\) |
| (c) | For \(A\) to move up the plane, \(\left(\theta\right)_{2}\) must always be greater than \(\left(\theta\right)_{1}\) |
| (d) | \(B\) will always slide down with a constant speed |
Which of the following statement/s is/are true?
| 1. | (b, c) | 2. | (c, d) |
| 3. | (a, c) | 4. | (a, d) |
A body of mass \(10\) kg is acted upon by two perpendicular forces, \(6\) N and \(8\) N. The resultant acceleration of the body is:
| (a) | \(1~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{4}{3}\right ) \) w.r.t. \(6\) N force |
| (b) | \(0.2~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{3}{4}\right ) \) w.r.t. \(8\) N force |
| (c) | \(1~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{3}{4}\right ) \) w.r.t. \(8\) N force |
| (d) | \(0.2~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{3}{4}\right ) \) w.r.t. \(6\) N force |
Choose the correct option:
1. (a), (c)
2. (b), (c)
3. (c), (d)
4. (a), (b), (c)
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 |
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 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. \(-5\left ( \hat{i} +\hat{j}\right ) \)
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