PART 1
QUESTION 01
An object of mass mis launched horizontally with a speed \(v\) at a height of h above the ground level as shown in figure below.
Let \(\theta\) be the impact angle to the ground and \(g\) be the acceleration of gravity. Find the formula of \(\tan \theta\).
(A) \(\dfrac {\sqrt{2gh}}{v}\)
(B) \(\dfrac {\sqrt{gh}}{2v}\)
(C) \(\dfrac {v}{\sqrt{2gh}}\)
(D) \(\dfrac {2v}{\sqrt{gh}}\)
(E) \(\dfrac {\sqrt{gh}}{v}\)
(F) \(\dfrac {v}{\sqrt{gh}}\)
QUESTION 02
An object of mass \(m\) is attached to a light spring with a force constant \(k\) and a natural length \(l_o\). The object is moving on a frictionless flat horizontal table with a uniform circular motion as shown in figure below. The center of the circle \(O\) is at the other end of the spring. During this motion, the length of the spring is extended by \(\alpha l_o ( \alpha > 0)\) from the natural length. Find the speed \(v\) of the object.
(A) \(\sqrt{\dfrac{(1 + \alpha) \alpha m}{k}} l_o\)
(B) \(\sqrt{\dfrac{m}{k}} (1 + \alpha) l_o\)
(C) \(\sqrt{\dfrac{m}{k}} \alpha l_o\)
(D) \(\sqrt{\dfrac{k}{m}} (1 + \alpha) l_o\)
(E) \(\sqrt{\dfrac{(1 + \alpha) \alpha k}{m}} l_o\)
(F) \(\sqrt{\dfrac{k}{m}} \alpha l_o\)
QUESTION 03
A charged particle of mass \(m\) and charge \(q\) is in a uniform electric field \(E\). Initially the particle is at rest, and then accelerated by the electric field. Find the time for the particle to travel at a distance of \(d\) from the initial location.
(A) \(\dfrac{md}{2qE}\)
(B) \(\sqrt{\dfrac{md}{qE}}\)
(C) \(\dfrac{md}{qE}\)
(D) \(\sqrt{\dfrac{md}{2qE}}\)
(E) \(\dfrac{md}{qE}\)
(F) \(\sqrt{\dfrac{2md}{qE}}\)
QUESTION 04
A screen is placed at a large distance \(L\) from a plate where two slits \(\text{S}_{\text{1}}\) and \(\text{S}_{\text{2}}\) are notched. These slits are separated by a distance of \(d\) as shown in figure below. A monochromatic light from a single slit \(\text{S}_{\text{0}}\) with a wavelength of \(\alpha\) passes through the two slits \(\text{S}_{\text{1}}\) and \(\text{S}_{\text{2}}\). Bright and dark interference fringes appear on the screen. Find the distance from the screen center \(\text{O}\) to the third dark line.
(A) \(\dfrac{L \lambda}{d}\)
(B) \(\dfrac{2 L \lambda}{d}\)
(C) \(\dfrac{3 L \lambda}{d}\)
(D) \(\dfrac{L \lambda}{2 d}\)
(E) \(\dfrac{3 L \lambda}{2 d}\)
(F) \(\dfrac{5 L \lambda}{2 d}\)
QUESTION 05
An observer is moving away at a constant speed of 5 m/s from a speaker which is emitting sound waves at a frequency of 660 Hz. The sound speed is 330 m/s. When the sound source S and the observation point O are located as shown in figure below, what frequency of the sound will the observer hear?
(A) 650 Hz
(B) 652 Hz
(C) 654 Hz
(D) 660 Hz
(E) 666 Hz
(F) 668 Hz