A car is moving along a circular road at speed of 20 m/s.The radius of the circular road is 10 m. If the speed is increased at the rate of 30 m/s², what is the resultant acceleration ?

10 m/s²
50 m/s²
250 m/s²
80 m/s²

Solution

A river 4.0 miles wide is flowing at the rate of 2 miles/ hr.The minimum time taken by a boat cross the river with a speed v = 4 miles/ hr (in still water) is approximately

1 hr
2 hr and 7 minutes
1 hr and 13 minutes
2 hr and 25 minutes

Solution

Note : According to the given question, no specific direction of motion is given. Therefore minimum time taken= 4/4 = 1 hr, when boat move right across the flow.

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

cannot be predicted
are equal to each other
are equal to each other in magnitude
are not equal to each other in magnitude

Solution

The coordinates of a moving particle at any time t are given by x = a t² and y = b t². The speed of the particle is

2 t(a + b)
\(2t\sqrt{(a^{2}+b^{2})}\)
\(2t\sqrt{(a^{2}-b^{2})}\)
\(\sqrt{(a^{2}+b^{2})}\)

Solution

The velocity of a projectile at the initial point A is \((2\hat{i}+3\hat{j})\) m/s. It’s velocity (in m/s) at point B is

\(-2\hat{i}+3\hat{j}\)
\(2\hat{i}-3\hat{j}\)
\(2\hat{i}+3\hat{j}\)
\(-2\hat{i}-3\hat{j}\)

Solution

At point B the direction of velocity component of the projectile along Y - axis reverses.

Hence,\(\overrightarrow{V_{B}}=2\hat{i}-3\hat{j}\)

A projectile is fired at an angle of 45° with the horizontal.Elevation angle of the projectile at its highest point as seen from the point of projection is

60°
tan^-1(¹⁄₂)
tan^-1(^√3⁄₂)
45°

Solution

Two stones are projected from the same point with same speed making angles 45° + θ and 45° – θ with the horizontal respectively. If θ ≤ 45, then the horizontal ranges of the two stones are in the ratio of

1 : 1
1 : 2
1 : 3
1 : 4

Solution

Note that the given angles of projection add upto 90°.So, the ratio of horizontal ranges is 1: 1.

The circular motion of a particle with constant speed is

periodic but not simple harmonic
simple harmonic but not periodic
periodic and simple harmonic
neither periodic nor simple harmonic

Solution

In circular motion of aparticle with constant speed,particle repeats its motion after a regular interval of time but does not oscillate about a fixed point. So,motion of particle is periodic but not simple harmonic.

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in 44 seconds, what is the magnitude and direction of acceleration of the stone?

π² m s^-2 and direction along the radius towards the centre.
π² m s^-2 and direction along the radius away from the centre.
π² m s^-2 and direction along the tangent to the circle.
π²/4 m s^-2 and direction along the radius towards the centre.

Solution

If the angle between the vectors \(\overrightarrow{A}\) and \(\overrightarrow{A}\) is θ, the value of the product \((\overrightarrow{B}\times \overrightarrow{A}).\overrightarrow{A}\) is equal to

BA² sinθ
BA² cosθ
BA² sinθ cosθ
Zero

Solution

\((\overrightarrow{B}\times \overrightarrow{A}).\overrightarrow{A}=\overrightarrow{C}.\overrightarrow{A}=CA\, Cos90^{\circ}=0\)

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