BPHCT-131 EM 2025 SOLVED ASSIGNMENT

Description

Tutor Marked Assignment
MECHANICS
Course Code: BPHCT-131
Assignment Code: BPHCT-131//TMA/2025
Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.
PART A
1. a) Determine the torque about the point (0, 1, 1) due to a force k j i F ˆ ˆ ˆ 2   

being exerted
at the point (4, 2, 3). (5)
b) Given two vector functions k j i a ˆ 2 ˆ ) 4 3 ( ˆ ) ( ) ( 2 3 t t t t t       and
, ˆ ) 6 ( ˆ ) 6 4 ( ˆ ) 7 ( ) ( 3 2 k j i b t t t t     

determine the derivative of a .b ( ) ( ) t t
  at . 1  t (5)
2. Solve the following ordinary differential equations:
a) 0 3 2 2 4 2 2      
  
  
  
 x y dx
dy yx (5)
b)

0 13 6 2
2
   y dx
dy
dx
y d for 2 ) 0 (  y , 3 4   
  
 y . (10)
3. a) A box of mass 10 kg is being pulled on the floor by a mass-less rope with a force of 100
N at an angle of 60 to the horizontal. What is the acceleration of the box if the coefficient
of kinetic friction between the floor and the box is ? 25 . 0  k Take . ms 10 2   g (5)
b) A ball having a mass of 0.5 kg is moving towards the east with a speed of velocity
6.0 ms-1. After being hit by a bat it changes its direction and starts moving towards
the north with a speed of 5.0 ms-1. If the time of impact is 0.1 s, calculate the
impulse and average force acting on the ball. (5)
c) A block of mass 5.0 kg starts from rest and slides down a surface which corresponds to a
quarter of a circle of 3.0 m radius. (i) If the curved surface is smooth, find the speed at the
bottom. (ii) If the speed at the bottom is 2.0 ms-1, calculate the energy dissipated due to
friction in the descent. (iii) After the block reaches the horizontal with a speed of 2.0 ms-1it
slides to a stop in a distance of 1.5 m. calculate the frictional force acting on the horizontal
surface. Take . ms 10 2   g (10)

d) A small satellite is in a circular orbit around a planet at a distance of m 10 0 . 4 8  from the
centre of the planet. The orbital speed of the satellite is . ms 200 1  What is the mass of the
planet? (5)

4

PART B
4. a) A solid cylinder of mass 3.0 kg and radius 1.0 m is rotating about its axis with a
speed of 40 rad s-1. Calculate the torque which must be applied to bring it to rest in
10s. What would be the power required? (10)
b) A proton undergoes a head on elastic collision with a particle of unknown mass
Initially at rest and rebounds with 16/25 of its initial kinetic energy. Calculate the
ratio of the mass of the unknown particle with respect to the mass of the proton. (10)
c) The planet Jupiter has an elliptical orbit e =.05 and a semi major axis of
m 10 8 . 7 11  . Find the energy of the planet and the perihelion and aphelion
distances. (5)
5. a) A simple harmonic oscillator has amplitude 15 cm and it completes 100 oscillations
in 50 s. (i) Calculate its time period and angular frequency. (ii) If the initial phase is
/2, write expressions for its displacement and velocity. (iii) Calculate the values of
maximum velocity and acceleration. (2+4+4)
b) For a damped harmonic oscillation, the equation of motion is
0 2
2
    kx dt
dx
dt
x d m
with kg, 25 . 0  m 1 kgs 05 . 0    and . Nm 70 1   k Calculate (i) the period of motion,
(ii) number of oscillations in which its amplitude will become half of its initial value,
and (iii) the number of oscillations in which its mechanical energy will drop to half of
its initial value. (2+4+4)
c) The equation of transverse wave on a rope is
y(x, t) = 10 sin (6.0t − 0.05x)
where y and x are measured in cm and t is expressed in second. Calculate the
maximum speed of a particle on the rope. (5)
*******