A block of mass M has a circular cut with a frictionless surface as shown. The block restson the horizontal frictionless surface of a fixed table. Initially the right edge of the block isat x = 0, in a co-ordinate system fixed to the table. A point mass m is released from rest atthe topmost point of the path as shown and it slides down. When the mass loses contactwith the block, its position is x and the velocity is v. At that instant, which of the followingoptions is/are correct?[A] The position of the point mass m is: 𝑥 = − 2 !"!!![B] The velocity of the point mass m is: 𝑣 = !!"!! !![C] The x component of displacement of the center of mass of the block M is: − !"!!![D] The velocity of the block M is: 𝑉 = − !! 2𝑔𝑅

A block is moving on a frictionless floor in the positive x-axis direction with an initial velocity of 12 m/s.  A constant force of 30 N directed along the negative x-axis acts on the block, and at the end of 8 s the block moves with a velocity of 4 m/s in the negative x-direction. Find the mass of the body.

A small block slides with velocity 0.5√gr on the horizontal frictionless surface as shown in the Figure. The block leaves the surface at point C. The angle θ in the Figure is:

A block with mass m1 = 0.400 kg is released from rest on a frictionless track at a distance h1 = 3.00 m above the top of a table. It then collides elastically with an object having mass m2 = 0.800 kg that is initially at rest on the table, as shown in the figure below.A curved wedge rests on a table. The wedge has the appearance of a hill sliced vertically in half: the surface at the top is horizontal, and then it gradually increases the magnitude of its slope down to the right before turning sharply down, and then decreasing the magnitude of its slope until it is almost horizontal. The vertical distance between the surface of the table and the top of the wedge is h1. The height of the table is h2. A block labeled m1 rests on the top of the wedge. A block labeled m2 rests at the very bottom of the slope of the wedge, at the edge of the table. A dashed parabolic line shows the path m2 would take after being knocked off the table. The path ends a horizontal distance x from the edge of the table.(a) Determine the velocities of the two objects just after the collision. (Assume the positive direction is to the right. Indicate the direction with the signs of your answers.)v1 = m/sv2 = m/s(b) How high up the track does the 0.400-kg object travel back after the collision? m(c) How far away from the bottom of the table does the 0.800-kg object land, given that the height of the table is h2 = 1.95 m? m(d) How far away from the bottom of the table does the 0.400-kg object eventually land? m

Block A𝐴 in (Figure 1) has mass 1.00 kgkg, and block B𝐵 has mass 3.00 kgkg. The blocks are forced together, compressing a spring S𝑆 between them; then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. Block B𝐵 acquires a speed of 1.30 m/sm/s.Figure1 of 1Part AWhat is the final speed of block A𝐴?Express your answer in meters per second.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typev𝑣 =nothingm/sm/sSubmitRequest AnswerPart BHow much potential energy was stored in the compressed spring?Express your answer in joules.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeU𝑈 =

A 1.5 kg block is initially at rest on a  horizontal frictionless surface when a  horizontal force along an x  axis is applied to the block. The force is given by F→ (x) = (2.5 − x 2 ) ˆ i N, where x is in meters and the initial position of the block is x = 0. (a) What is the kinetic energy of the block as it passes through x = 2.0 m? (b) What is the maximumkinetic energy of the block between x = 0 and x = 2.0 m?