Engineering Mechanics – 4
91. A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles.
The total flow rate Q through the sprinkler is 1 litre/sec and the crosssectional area of each exit nozzle is 1 cm^{2}. Assuming equal flow rate through both arms and a frictionless hinge, the steady state angular speed of rotation (in rad/s) of the sprinkler is ______ (correct to two decimal places).
(2 Mark, 2018[1])

Ans: 10
Explanation:
92. A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in m/s^{2}) of the centre of the disc is ________ (correct to two decimal places).
(2 Mark, 2018[2])

Ans: 6.67
Taking moment about the point of contact, F\times r=I\alpha
F\times r=I\times \frac { a }{ r } ………….(1)
MOI of the disc about the point of contact,
I = \frac { M{ r }^{ 2 } }{ 2 } +M{ r }^{ 2 }=\frac { 3 }{ 2 } M{ r }^{ 2 }
=> I = \frac { 3 }{ 2 } \times 10\times { 1 }^{ 2 } = 15 kg{ m }^{ 2 }
Now equation (1) becomes,
100\times 1 = 15\times \frac { a }{ 1 }
=> a = 6.67 m/{ s }^{ 2 }
93. The position vector \overrightarrow { OP } of point P (20, 10) is rotated anticlockwise in XY plane by an angle θ = 30^{0} such that point P occupy position Q, as shown in the figure. The coordinates (x, y) of Q are
(a) (13.40, 22.32)
(b) (12.32, 18.66)
(c) (22.32, 8.26)
(d) (18.66, 12.32)
(1 Mark, 2019[1])

Ans: c
Explanation:
94. A block of mass 10 kg rests on a horizontal floor. The acceleration due to gravity is 9.81 m/s^{2}. The coefficient of static friction between the floor and the block is 0.2.
A horizontal force of 10 N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is _____.
(1 Mark, 2019[1])

Ans: 10
Explanation:
95. A car having weight W is moving in the direction as shown in the figure. The centre of gravity (CG) of the car is located at height h from the ground, midway between the front and rear wheels.
The distance between the front and rear wheels is l. The acceleration of the car is a, and acceleration due to gravity is g. The reactions on the front wheels (R_{f}) and rear wheels (R_{r}) are given by
(a) { R }_{ f }={ R }_{ r }=\frac { W }{ 2 } +\frac { W }{ g } \left( \frac { h }{ l } \right) a
(b) { R }_{ f }=\frac { W }{ 2 } +\frac { W }{ g } \left( \frac { h }{ l } \right) a, { R }_{ r }=\frac { W }{ 2 } \frac { W }{ g } \left( \frac { h }{ l } \right) a
(c) { R }_{ f }={ R }_{ r }=\frac { W }{ 2 } \frac { W }{ g } \left( \frac { h }{ l } \right) a
(d) { R }_{ f }=\frac { W }{ 2 } \frac { W }{ g } \left( \frac { h }{ l } \right) a, { R }_{ r }=\frac { W }{ 2 } +\frac { W }{ g } \left( \frac { h }{ l } \right) a
(2 Mark, 2019[1])

Ans: c
Explanation:
96. A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of 10 kN is applied at point D. The magnitude of force (in kN) in the member BC is _____.
(2 Mark, 2019[1])

Ans: 5
Explanation:
97. The figure shows an idealized plane truss. If a horizontal force of 300N is applied at point A, then the magnitude of the force produced in member CD is _____N.
(1 Mark, 2019[2])

Ans: 0
By using the concept of zero force member in a truss, we will find the members like BC, CD, DE, EF are zero force members.
98. A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectlyelastic directcentral impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value (s) of m is/are
(a) 6 kg only
(b) 1kg, 9 kg
(c) 1 kg, 6 kg
(d) 1 kg only
(2 Mark, 2019[2])

Ans: d
Explanation: