Physics Laws of Motion

A body of mass 2kg moves under a force of (2i + 3j + 5k)N. It starts from rest and was at the origin initially. After 4 s, its new coordinates are (8, b, 20). The value of b is --------. (Round off the Nearest Integer)

Statement I: A cyclist is moving on an un-banked road with a speed of 7 kmh?¹ and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2 The cyclist will not slip and pass the curve. (g = 9.8m/s²)
Statement II: If the road is at an angle of 45°, cyclist can cross of the curve of 2m radius with the speed of 18.5 kmh?¹ without slipping
In the light of the above statements, choose the correct the answer from the options given below.

A small block slides down from the top of hemisphere of radius R = 3m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is _____ m. (Assume there is no friction between the block and the hemisphere)

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle θ as shown in figure. The coefficient of kinetic is μ_k . Then, the block's acceleration 'a' is given by :

(g is acceleration due to gravity)

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is:

A force F = (40î + 10?)N acts on a body of mass 5 kg. If the body starts from rest, its position vector r at time t = 10s, will be :

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is :
(Diagram shows ball 'a' hitting the wall perpendicularly along the x-axis and ball 'b' hitting the wall at a 45° angle to the x-axis.)

An inclined plane in bent in such a way that the vertical cross-section is given by y  where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction = 0.5, the maximum height in cm at with a stationary block with not skip downward is ____________cm.

The coefficient of static friction between a wooden block of mass 0.5kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall be__________ N.

A person standing on a balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of 1.8m/s² will be----------N. [g = 10 m/s²]