Ship A is moving westward with a speed of \(10\ \text{km h}^{- 1}\) and Ship B, \(100 \ \text{km}\)south of A, is moving northwards with a speed of \(10\ \text{km h}^{- 1}\)${\mathrm{}}^{}$. The time after which the distance between them becomes the shortest is:

1. \(5\) hr

2. \(5 \sqrt2\) hr

3. \(10 \sqrt2\)$\mathrm{}$ hr

4. \(0\) hr

A particle projected with kinetic energy ${\mathrm{k}}_0$ with an angle of projection $\mathrm{\theta }$. Then the variation of kinetic K with vertical displacement y is

1.  linear

2.  parabolic

3.  hyperbolic

4.  periodic

A particle starts from the origin at \(t=0\) and moves in the \(x-y\) plane with constant acceleration \(a\) in the \(y\) direction. Its equation of motion is \(  𝑦 = 𝑏 𝑥^2\). The \(x\) component of its velocity \((\text{at} \ t=0) \) is:

1. Variable

2. \(\sqrt{\dfrac{2a}{b}}\)

3. \(\dfrac{a}{2b}\)

4. \(\sqrt{\dfrac{a}{2b}}\)

A particle has initial velocity $\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right)$ and has acceleration $\left(0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}\right)$. Its speed after 10 s:

1. 7 units

2. $7\sqrt{2}$ units

3. 8.5 units

4. 10 units

The gravity in space is given by \(\vec g=-10 \hat j\ \text{m/s}^{2}\). Two particles are simultaneously projected with velocity \(\vec u_1=10\ \text{m/s} \hat i+10\ \text{m/s} \hat j\) and \(\vec u_2=20\ \text{m/s} \hat i+10\ \text{m/s} \hat j\). Then, the ratio of their times of flight is:

1. \(1:1\)

2. \(1:2\)

3. \(2:1\)

4. None of the above

A train is moving towards the east and a car is along the north at the same speed. The observed direction of the car to the passenger on the train is:

Two racing cars of masses \(m_1\) and \(m_2\) are moving in circles of radii \(r_1\) and \(r_2\) respectively. Their speeds are such that each makes a complete circle in the same duration of time \(t\). The ratio of the angular speed of the first to the second car is:

A particle \(P\) is moving in a circle of radius \(a\) with a uniform speed \(v\). \(C\) is the centre of the circle and \(AB\) is a diameter. When passing through \(B\) the angular velocity of \(P\) about \(A\) and \(C\) are in the ratio:

1. \(1 : 1\)

2. \( 1 : 2\)

3. \(2 : 1\)

4. \(4 : 1\)

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is 

1. R/r

2. r/R

3. R²/r²

4. r²/R²

An electric fan has blades of length \(30\ \text{cm}\) as measured from the axis of rotation. If the fan is rotating at \(1200\ \text{r.p.m}\), the acceleration of a point on the tip of the blade is about:

1. \(1600\ \text{m/s}^2\)

2.  \(4740\ \text{m/s}^2\)

3. \(2370\ \text{m/s}^2\)

4. \(5055\ \text{m/s}^2\)