Part -6 Motion in a plane hard

A body is projected from the ground at an angle of 60⁰ with the horizontal. The ratio of the maximum height attained by it to its horizontal range is-

A stuntman plans to run across a roof top and then horizontally off it to land on the roof of the next building. The roof of the next building is 4.9 m below the first one and 6.2 m away from it. The minimum roof top speed for successful jump is -

A projectile is thrown with velocity v at an angle θ with the horizontal. When the projectile is at a height equal to half of the maximum height, then the vertical component of the velocity of projectile is -

A ball rolls of the top of the stair way with a horizontal velocity u ms^–1. If the steps are h m high and b m wide, the ball will hit the edge of the nth step, if -

A body is projected at an angle 30⁰ to the horizontal with speed 30 m/s. What is the angle with the horizontal after 1.5 seconds? (g = 10 m/s²)

A body is projected horizontally with speed 20 m/s. What will be its speed nearly after 5 sec?

If a projectile thrown with a speed v at an angle 45⁰ to the horizontal attains a maximum height of 6.2m, its range will be -

A ball is rolled off the edge of a horizontal table at a speed of 4 m/s. It hits the ground after 0.4 sec. Which statement given bellow is true ?

Take the z-axis as vertical and the xy plane as horizontal. A particle A is projected at 4√2 m/s at an angle of 45⁰ to the horizontal, in the xz plane. Particle B is projected at 5 m/s at an angle θ= tan^–1(4/3) to the y-axis, in the yz plane. Which of the following is not correct for the velocity of B with respect to A?

The equation of motion of a projectile is, y = 12x – 3/4x²

The horizontal component of velocity is 3 m s^–1. Given that g = 10 m s^–2, what is range of the projectile?

Two racing cars of masses m₁ and m₂ are moving in circles of radii r and 2r respectively and  their angular speeds are equal. The ratio of the time taken by cars to complete one revolution is :

A particle moves along a circle of radius (20/π) m with tangential acceleration of constant magnitude. If the speed of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is:

Two particles P and Q are located at distances r_P and r_Q respectively from the axis of a rotating disc such that r_P > r_Q :

Let a_r and a_t represent radial and tangential acceleration. The motion of a particle may be circular if :

If the radii of circular paths of two particles of same masses are in the ratio of 1 : 2, then in order to have same centripetal force, their speeds should be in the ratio of :

A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal smooth surface. The maximum tension the string can withstand is 16 N. The maximum speed of revolution of the stone without breaking it, will be :

On horizontal smooth surface a mass of 2 kg is whirled in a horizontal circle by means of a string at an initial angular speed of 5 revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new angular speed is nearly:

A particle is kept fixed on a uniformly rotating turn-table As seen from the ground , the particle goes in a circle, its speed is 10 cm/s and acceleration is 10 cm/s².The particle is now shifted to a new position to make the radius half of the original value.The new values of the speed and acceleration will be

A rod of length L is hinged at one end and it is rotated with a constant angular velocity in a horizontal plane . Let T₁ and T₂ be the tensions at the points L/4 and 3L/4 away from the hinged end.

A particle moving along a circular path due to a centripetal force having constant magnitude is an example of motion with :

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles 30° and 60° from downward vertical are T₁ and T₂ Then

A bucket is whirled in a vertical circle with a string attached to it.The water in bucket does not fall down even when the bucket is inverted at the top of its path. In this position choose most appropiate option if v is the speed at the top.