Engineering Physics-I Mid-Term Exam 2023 PDF

# SCHOOL OF ENGINEERING AND TECHNOLOGY ## D.C. COURT JUNCTION, DIMAPUR ### MID-TERM EXAMINATIONS, October 2023 ## Course Code: G1T02 ## Semester: I ## Course Name: Engineering Physics-I ## Total: 30 Marks ## Time: 1/2 hours ### **Part - A** **Q.1. Answer the following questions** (5...

# SCHOOL OF ENGINEERING AND TECHNOLOGY ## D.C. COURT JUNCTION, DIMAPUR ### MID-TERM EXAMINATIONS, October 2023 ## Course Code: G1T02 ## Semester: I ## Course Name: Engineering Physics-I ## Total: 30 Marks ## Time: 1/2 hours ### **Part - A** **Q.1. Answer the following questions** (5 x 1 = 5) * **a.** A man is standing on a disc at a distance of 3 m from the disc's centre. The disc itself is rotating around its centree at constant angular speed of π rad/s. The speed of the man with respect to the ground is * (i) 3 ms-1. * (ii) π ms-1. * (iii) 3π ms-1. * (iv) 3π2 ms-1. * **b.** The dimensions of energy are: * (i) ML²T⁻² * (ii) ML⁻¹T⁻² * (iii) ML²T⁻¹ * (iv) ML⁻²T⁻² * **c.** Suppose a force F = -3i +2j -k N acts on a particle of mass 3 kg. The acceleration of the particle is (give the vector expression): * (ms⁻²) * **d.** A ball of mass 5 kg is moving in the positive X direction with a speed of 2 m/s. Soon, it collides with a ball of mass 3 kg moving in the negative X direction with a speed of 4 m/s. Suppose that after collision the two balls stick together. Then the combined system continues moving in the direction: * (i) positive X * (ii) negative X * (iii) positive Y * (iv) negative Y. * **e.** In the air wedge experiment, the band lying on the line of intersection of the two glass plates (where the thickness of air film is zero) is * (i) full dark * (ii) fill bright * (iii) almost full bright * (iv) almost full dark ### **Part - B** **Q. 2. Answer any three questions** (3 x 3 = 9) **a.** Find the centre of mass of a hydrogen sulphide molecule H2S. For simplicity assume that the two sulphur-hydrogen bonds subtend an angle of 90°, each bond has a length of 2.5 x 10⁻¹⁰ m and the sulphur atom is 32 times heavier than a hydrogen atom. **b.** A ball of mass m is moving with speed 3v in the positive X direction. Another ball of mass 2m is moving with speed 2v in the negative X direction. They collide at the origin at time t = 0. Suppose the collision is elastic. Describe the motions i.e. the speeds and directions of the two balls after the collision. **c.** Consider a Young's double slit experiment in which the two slits are 0.5 mm apart and the screen is 2 m from the slits. The fourth bright fringe is 10 mm from the central bright fringe. Find the wavelength of light. **d.** Cars B and C have the same mass. Car A has half the mass of Car B. As shown, cars B and C have a small gap between them initially and they are at rest with their brakes off. **e.** Car A plows into B at high speed, pushing B into C. If all collisions are completely inelastic, what fraction of the initial kinetic energy of car A is dissipated when car C is struck? ### **Part - C** **Q.3. Answer the following questions** **a.** Suppose the two glass plates of the air wedge experiment shown in the figure are each 15 cm long. At one end they are in contact; at the other end they are separated by a piece of paper 0.1 mm thick. Monochromatic light with a wavelength in air of λ = 600 nm is shining on the system. The refractive index of glass is ng = 1.5. *(a)* What is the spacing of the interference fringes seen by reflection? Is the fringe at the line of contact bright or dark? *(b)* Now suppose the thin wedge between the glass plates gets filled by water due to a spill. Water has a refractive index of nw = 1.3. What is the spacing of the interference fringes now? Is the fringe at the line of contact bright or dark now? **b.** Consider a particle moving along a circle of radius b. The motion of the particle is such that at time t its angular coordinate is θ(t) = at², where a > 0. Find the velocity vector of the particle in cartesian coordinates at a time to > 0. **c.** Consider the same setting as the previous problem. Now suppose that a force F, shown in red on the left, acts on the particle in a direction halfway between the ∠ and 6 unit vectors, shown in blue on the left. At time t, the force F has magnitude ct, where c > 0. What is the work done by the force on the particle from time t = 0 till time t = to?