Q- A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T, as shown. Derive a formula for the bullet speed v in terms of D, T and a measured angle θ between the position of the hole in the first disk and that of the hole in the second.…

## Solution Search

## . : "Mechanics"

### Mechanics: Center of Mass and Momentum

Q- Two masses 5 kg and 15 kg are moving along x direction with velocities of 10 m/s and 2 m/s respectively. At an instant they are at positions 10 m and 70 m respectively

(A) Find position of their center of mass at this instant.

(B) If the two will collide inelastically what is their common velo…

### Variable Mass: Conservation of Momentum

Q- A mass in the form of a solid cylinder, of radius R acted upon by no forces, moves parallel to its axis through a uniform cloud of fine dust, of volume density ρ, which is at rest. If the particles of dust which meet the mass adhere to it, and if M and u be the mass and the velocity at the begi…

### Mechanics: Translation and Rotation

Q- Block A of mass m = 10 kg is pulled from rest, on a horizontal surface by a massless rope passing over a pulley of same mass m = 10 kg, radius R = 0.25 m and moment of inertia I = 1.2 kg m2, rotates freely about its axis. The force applied at the end of the rope is P = 750 N. If the coefficient…

### Center Of Mass

Q- Three particles, each with a mass of 0.25 kg, are located at ( - 4.0 m, 0), (2.0 m, 0), and (0, 3.0 m) and are acted on by forces F_{1} = 3 N along negative y-direction, F_{2} = 5 N along positive y-direction and F_{3} = 4 N along x direction respectively. Find position of center of mass of the system a…

### Head-on Collision

Q- A 1000 kg car traveling east at 25 mph gets rear-ended hit by a truck weighing 1500 kg also moving east. After collision the vehicles lock bumpers and continue moving east at 40 mph.

(a) What was the original speed of the truck

(b) How much kinetic energy of the system lost during this collisi…

### Mechanics: Conservation Of Energy

(On request - Manish)

Q- Two blocks are connected by a light cord passing over a frictionless pulley. Their masses are m_{1} = 3 kg and m_{2} = 2 kg and the ramp is frictionless. At position A the block m_{1} is sliding up at velocity 2.5 m/s. Find the speed of the block at position B.

### Circular Motion

Q- A disk accelerates constantly from rest. After 8 s, it has made 3 revolutions.

(a) What is the angular acceleration of the disk?

(b) What is the angular velocity of the disk at t = 8 s?

(c) If the radius of the disk is 50 cm, what is the linear velocity of a point on the rim at time t = 8 s?

### Mechanics: Conservation of Energy

Q- A roller coaster car of mass 1000 kg is riding along a track from point A to point C as in figure. (g = 10 m/s^{2})

(a) Assuming no friction between the track and the car, what is the speed of the car at the top of first hill A?

(b) What is the speed of the car at the top of second hill B?

(c) Wh…

### Collision

Q- A truck with mass 5000 kg is heading east at 20 m/s. Meanwhile a car with mass 2500 kg is heading north at 30 m/s. The two vehicles collide at an intersection, get stuck together and the wreckage keeps moving to some direction.

(a) Is the collision elastic or inelastic?

(b) Find the speed of th…

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Abhigyan Martin NinamaRohit DewalAjay kumar