Motion In Plane

A and B are two vectors and θ is the angle between them, if ｜A x B｜=√3(A･B), the value of θ is

The horizontal range and maximum height of a projectile are equal. The angle of projection is

If two vectors 2i+3j+k and -4i-6j-λk are parallel to each other, then the value of λ is

If A = 3i+4j and B = 7i+24j the vector having the same magnitude as B and parallel to A is

A missile is fired for maximum range with an initial velocity of 20 m/s. If g=10 m/s², the range of missile is

If a vector 2i+3j+8k is perpendicular to the vector 4j-4i+αk, then value of α is

The angle between the two vectors A = 3i+4j+5k and B = 3i+4j-5k will be

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is :

If A=4i+4j+4k and b=3i+j+4k, then angle between vectors A and B is

If two vectors are equal in magnitude and their resultant is also equal in magnitude to one of them, then the angle between the two vectors is

The horizontal range and maximum height attained by a projectile are R and H, respectively. If a constant horizontal acceleration a=g/4 is imparted to the projectile due to wind, then it’s horizontal range and maximum height will be

A projectile is thrown in the upward direction making an angle of 60° with the horizontal direction with a velocity of 147 m/s. Then, the time after which its inclination with the horizontal is 45°, is

A rocket is fired upward from the earth surface such that it creates an acceleration of 19.6 m/s². If after 5s, its engine is switched off, the maximum height of the rocket from earth’s surface would be

A particle is moving such that its position coordinates (x,y) are (2 m,3 m) at time t=0,(6 m,7 m) at time t=2 s and (13 m,14 m) at time t=0 to t=5 s is

A piece of marble is projected from the earth’s surface with velocity of 50 m/s. 2s later, it just clears a wall 5m high. What is the angle of projection?

A ball is projected upwards from the foot of a tower. The ball crosses the top of the tower twice after an interval of 6 s and the ball reaches the ground after 12 s. The height of the tower is (take, g= 10 ms⁻² )

A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from earth. The value of the acceleration due to gravity on the planet is (in m/s²). (Given ,g= 9.8 m/s²)

A ball is moving in a circular path of radius 5m. If tangential acceleration at any instant is 10 m/s ² and the net acceleration makes an angle 30° with the centripetal acceleration, then the instantaneous speed is

A wheel is rotating at 900 rpm about its axis. When the power is cut-off it comes to rest in 1 min. The angular retardation in rad s⁻² is

An inclined plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to

A particle of mass m is projected with a velocity v making an angle of 45° with the horizontal. The magnitude of angular momentum of projectile about the point of projection when the particle is at its maximum height h is

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

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ?.Four objects each of mass m, are kept gently to the opposite ends oftwo perpendicular diametres ofthe ring.The angular velocity of the ring will be

A particle performing uniform circular motion has angular momentum L.If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be:

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 particle has initial velocity (2î + 3ĵ) and acceleration (0.3î + 0.2ĵ).  The magnitude of velocity after 10 seconds will be:

At what angle should the two forces 2P and √2 Pact, so that the resultant force is P√10?

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends.The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity?. The force exerted by the liquid at the other end is

When a ceiling fan is switched on, it makes 10 revolutions in the first 3s. Assuming a uniform angular acceleration, how many rotation it will make in the next 3s?

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 performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

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