A particle moving with uniform speed in a circular path maintains:

(1). Constant velocity
(2). Constant acceleration
(3). Constant velocity but varying acceleration
(4). Varying velocity and varying acceleration

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A ball is projected with a velocity, \(10\, ms^{−1} \), at an angle of \( 60^\circ \) with the vertical direction. Its speed at the highest point of its trajectory will be

(1). Zero
(2). \(5 \sqrt{3}\, ms^{-1} \)
(3). \(5 \,ms^{-1} \)
(4). \(10 \,ms^{-1} \)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' θ ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, θ, is then given by:

(1). \( \theta = {\cos^{-1} \left( \frac{gT^2}{\pi^2 R} \right)}^{1 / 2} \)
(2). \( \theta = {\cos^{-1} \left( \frac{\pi ^2R}{gT^2} \right)}^{1 / 2} \)
(3). \( \theta = {\sin^{-1} \left( \frac{\pi ^2R}{gT^2} \right)}^{1 / 2} \)
(4). \( \theta = {\sin^{-1} \left( \frac{2gT^2}{\pi^2 R} \right)}^{1 / 2} \)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

(1). \( 45^\circ \)
(2). \( 180^\circ \)
(3). \( 0^\circ \)
(4). \( 90^\circ \)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A bullet is fired from a gun at the speed of 280 cm\( s^{−1} \) in the direction \( 30^\circ \) above the horizontal. The maximum height attained by the bullet is (\( g = 9.8 ms^{−2} \), \( Sin30^\circ \) = 0.5)

(1). 2000 m
(2). 1000 m
(3). 3000 m
(4). 2800 m

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The speed of a swimmer in still water is 20m ∕ s. The speed of river water is 10m ∕ s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given by

(1). \( 45^\circ \) west
(2). \( 30^\circ \) west
(3). \( 0^\circ \)
(4). \( 60^\circ \) west

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

When an object is shot from the bottom of a long smooth inclined plane kept at an angle \(60^\circ \) with horizontal, it can travel a distance \( {\text{x}_1} \) along the plane. But when the inclination is decreased to \(30^\circ \) and the same object is shot with the same velocity, it can travel \( {\text{x}_2} \) distance. Then \( {\text{x}_1}:{\text{x}_2} \) will be

(1). 1 : \(2\sqrt{3} \)
(2). 1 : \(\sqrt{2} \)
(3). \(\sqrt{2} \) : 1
(4). 1 : \(\sqrt{3} \)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

Two particles A and B are moving in uniform circular motion in concentric circles of radii \(r_A\) and \(r_B\) with speed \(v_A\) and \(v_B\) respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be

(1). \(1\, :\,1\)
(2). \(r_A\, :\,r_B\)
(3). \(v_A\, :\,v_B\)
(4). \(r_B\, :\,r_A\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

The x and y coordinates of the particle at any time are x = 5t − 2\(t^2 \) and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s

(1). \(\displaystyle 5 \, \frac{m}{s^2}\)
(2). \(\displaystyle - 4 \, \frac{m}{s^2} \)
(3). \(\displaystyle -8 \, \frac{m}{s^2}\)
(4). \(0\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02

A particle moves so that its position vector is given by \(\vec{r}\, =\, cos \,\omega \,t\, \hat{x}\, +\, sin\, \omega\,t\,\hat{y}\), where \(\omega\) is a constant. Which of the following is true ?

(1). Velocity is perpendicular to \(\vec{r}\) and acceleration is directed towards the origin
(2). Velocity is perpendicular to \(\vec{r}\) and acceleration is directed away from the origin
(3). Velocity and acceleration both are perpendicular to \(\vec{r}\)
(4). Velocity and acceleration both are parallel to \(\vec{r}\)

Number of Attempts: 2

Correct Attempts: 1

Time Taken: 00:04

Average Time: 00:02