A body of mass 2kg travels according to the law $\mathrm{x}\left(\mathrm{t}\right)=\mathrm{pt}+{\mathrm{qt}}^2+{\mathrm{rt}}^3$ where, $\mathrm{q}=4{\mathrm{ms}}^{-2},\mathrm{p}=3{\mathrm{ms}}^{-1}\text{ and }\mathrm{r}=5{\mathrm{ms}}^{-3}$. The force acting on the body at t=2s is

1. 136 N
2. 134 N
3. 158 N
4. 68 N

A body with a mass of \(5\) kg is acted upon by a force \(\vec{F}=\left ( -3\hat{i} +4\hat{j}\right )\) N. If its initial velocity at \(t=0\) is \(\vec{v}=\left ( 6\hat{i} -12\hat{j}\right )\) 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:

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 rn/2 and of B is m.

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 ${\mathrm{m}}_1$ moves on a slope making an angle $\mathrm{\theta }$ with the horizontal and is
attached to mass ${\mathrm{m}}_2$ by a string passing over a frictionless pulley as
shown in the figure. The coefficient of friction between ${\mathrm{m}}_1$ and the sloping
surface is $\mathrm{\mu }$.

$\begin{array}{l}\text{(a) If }{\mathrm{m}}_2>{\mathrm{m}}_1\sin \mathrm{\theta }\text{, the body will move up the plane.}\end{array}$
(b) If m₂>m₁(sin⁡θ+μcos⁡θ), the body will move up the plane.
(c) If m₂<m₁(sin⁡θ+μcos⁡θ), the body will move up the plane.
(d) If m₂<m₁(sin⁡θ−μcos⁡θ), the body will move down the plane.

Which of the following statement/s is/are true?

1. (a, d)

2. (a, c)

3. (c, d)

4. (b, 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:

$\begin{array}{l}\end{array}$
Choose the correct option:

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:

A cricket ball of mass 150 g has an initial velocity $\mathrm{u}=(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}){\mathrm{ms}}^{-1}$ and a  final velocity$\mathrm{v}=-(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}){\mathrm{ms}}^{-1}$, after being hit. The change in momentum (final momentum-initial momentum) is (in kgm/s)

\(1.~zero\)
\(2.~-\left ( 0.45\hat{i}+0.6\hat{j} \right ) \)
\(3.~-\left ( 0.9\hat{i}+1.2\hat{j} \right ) \)
\(4.~-5\left ( \hat{i} +\hat{j}\right ) \)

A meter scale is moving with uniform velocity. This implies: