✓✗The position vector of a particle as a function of time is given by where R is in meters, t is in seconds and and denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?

✓✗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

✓✗A train of 150 metre length is going towards north direction at a speed of 10 m/s. A parrot flies at the speed of 5 m/s towards south direction parallel to the railways track. The time taken by the parrot to cross the train is

✓✗A bus is moving on a straight road towards north with a uniform speed of 50 km/hour then it turns left through 90°. If the speed remains unchanged after turning, the increase in the velocity of bus in the turning process is

✓✗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

✓✗A projectile is fired from the surface of the earth with a velocity of 5 m s^–1 and angle q with the horizontal. Another projectile fired from another planet with a velocity of 3 m s^–1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m s^–2) is (Given g = 9.8 m s^–2)

✓✗A person aiming to reach exactly opposite point on the bank of a stream is swimming with a speed of 0.5 m/s at an angle of 120° with the direction of flow of water. The speed of water in the stream, is

✓✗A body is whirled in a horizontal circle of radius 20 cm. It has an angular velocity of 10 rad/s. What is its linear velocity at any point on circular path ?

✓✗A particle moves in x-y plane according to rule x = asinwt and y = acoswt. The particle follows

✓✗A particle shows distance-time curve as given in this figure.

The maximum instantaneous velocity of the particle is around the point

✓✗If then the value of is

✓✗Two racing cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂ respectively. Their speeds are such that each makes a complete circle in the same time t. The ratio of the angular speeds of the first to the second car is

✓✗A particle has initial velocity () and acceleration (). The magnitude of velocity after 10 seconds will be

✓✗A particle moves so that its position vector is given by , where w is a constant. Which of the following is true?

✓✗The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is