Mechanics | Relativity Answers

1. The figure attached is water fall which is 50 m high. Water falls in a section of the fall at the rate of 1.2×106kgs−1 . How much power is generated by the fall?

2 Calculate the volume contraction of 100 mL when subjected to a pressure of 1.5 MPa
a. 0.045 mL
b. -0.071 mL
c. 0.033 mL
d. -0.027 mL

Derive expression for average rate at which energy is transported by a progressive
wave propagating in a medium.

16 Which of the following is true about the skater
a. Her angular velocity increases when her arms are spread out because her hands exert a force on her body
b. Her angular velocity decreases when her arms are pulled close to her body because linear momentum is conserved
c. Her angular velocity increases when her arms are pulled close to her body because angular momentum is conserved
d. Her angular velocity decreases when her arms are spread out because angular energy is conserved.

17 Which of these laws must the restoring force of an oscillating system obey for it to be regarded as a simple harmonic oscillator?
a. Newton's first law of motion
b. Hooke's law of elasticity
c. The law of conservation of momentum
d. The law of conservation of matter

7 The system shown is an example of the Atwood's machine. m1 and m2 are connected by a light inextensible string over a light and smooth pulley with m1>m2. What is the acceleration of the masses?

12 A long light steel strip is clamp at the lower end and a 2.0-kg mass is fastened to the top end as shown in the figure. A horizontal force of 8.0 N is required to displace the mass to 20 cm one side. Assuming that the system undergoes simple harmonic motion when released, calculate the period of oscillation of the mass.

7. The system shown is an example of the Atwood's machine. m1 and m2 are connected by a light inextensible string over a light and smooth pulley with m1>m2. What is the acceleration of the masses?

1. The rope shown in the figure attached hereto is wound around a cylinder of of mass 4.0 kg, radius 10cm and I= 0020kgm2 , where I is the moment of inertia about an axis along the cylinder axis. If the cylinder rolls without slipping, what the linear acceleration of its centre of mass?

2. Three particles of masses m1=1.2kg, m2=2.5kg and m3=3.4kg
are at the vertices of an equilateral triangle of side a = 140 cm. Calculate the centre of mass of the system.

9. A particle of mass 1 kg moving with initial velocity
(i^+2k^) m/s is acted upon by a constant force
(i^+2j^−2k^) N. Calculate the velocity and distance after 5s.

18. A house is built on the top of a hill with a nearby 45 degrees slope as shown in the figure. An engineering study indicates that the slope angle should be reduced because the top layers of soil along the slope might slip past the lower layers. If the static coefficient of friction between two such layers is 0.5, what is the least angle ϕ through which the present slope should be reduced to prevent slipping?

14. Two people sit in a car that weighs 800 N as shown in the figure. The person at the front weighs 700 N while the one in the back weighs 900 N. The distance between the front and back wheels is L units. The centre of gravity of the car is 0.4L units behind the front wheel. How much force does each each front wheel and each back wheel of the car support if the people in the car sit along the centreline of the car?.
a. 2.09 kN, 2.71 kN
b. 4.11 kN, 5.22 kN
c. 5.021 kN, 4.31 kN
d. 1.42 kN, 3.72 kN

A basket ball player, 2.00 m tall, wants to make a goal 10 m from the basket as shown in the figure attached hereto. If he releases the ball at an angle of 45 degrees to the horizontal, at what initial velocity must he shoot the ball so that it goes through the hoop without striking the backboard?

25 m/s
10 m/s
45 m/s
100 m/s