76. A rope is wrapped twice around a rough pole with a coefficient of friction ‘A . It is subjected to a force F1 at one end and a gradually increasing force F2 is applied at the other end till the rope just starts slip-ping. At this instant the ratio of F2 to Fi is
a) 1
b) e2*
c) e4*
d) e*72
Ans: b
77. A ladder of weight ‘w’ rests against a smooth vertical wall, and rests on rough horizontal ground, the coefficient of friction between the ladder and the ground being 1/4. The maximum angle of incli¬nation of the ladder to the vertical, if a man of weight ‘w’ is to walk to the top of it safely, is tan’1 x, where x is
a) 1/4
b) 1/3
c) 3
d) 4
Ans: b
78. If a body is lying on a plane whose inclination with the horizontal is less than the angle of friction, then
i) a force is required to move the body upwards
ii) a force is required to move the body downward
iii) the body will not be in equilibrium
The correct answer is
a) only (i)
b) only (ii)
c) both (i) and (ii)
d) both (i) and (iii)
Ans: c
78. Intrinisic equation of catenary is given by
a) S = C tan q>
b) S = C cos cp
c) S = C sin cp
d) S = C cot <p
where C is some constant.
Ans: a
79. The shape of a suspended cable for a uniformly distributed load over it is
a) circular
b) parabolic
c) catenary
d) cubic parabola
Ans: b
80. Cartesian form of the equation of catenary is
a) y = c cosh x/c
b) y = c sinh x/c
c) y = c tan x/c
d) y = c sin”1 x/c
Ans: a
81. A cable loaded with 10 kN/m of span is stretched between supports in the same horizontal line 100 m apart. If the central dip is 10 m, then the maximum and minimum pull in the cable respectively are
a) 1346.3 kN and 1500 kN
b) 1436.2 kN and 1250 kN
c) 1346.3 kN and 1250 kN
d) 1436.2 kN and 1500 kN
Ans: c
82. Minimum pull in a suspended cable with supports at two ends is equal to
a) horizontal thrust
b) support reactions
c) resultant of horizontal thrust and support reaction
d) half the weight of the cable
Ans: a
83. A light rope is loaded with many equal weights at equal horizontal intervals. The points of suspension on the rope lie on a
a) parabola
b) catenary
c) cycloid
d) ellipse
Ans: a
84. The maximum pull in a cable, carrying a uniformly distributed load and supported at two ends which are at the same level, is at
a) supports
b) quarter span
c) mid span
d) none of the above
Ans: a
85. A ball moving on a smooth horizontal table hits a rough vertical wall, the coefficient of restitution between ball and wall being 1/3. The ball rebounds at the same angle. The fraction of its kinetic energy lost is
a) 1/3
b) 2/3
c) 1/9
d) 8/9
Ans: d
86. A particle is dropped from a height of 3 m on a horizontal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the ball will rebound after striking the floor is
a) 0.5 m
b) 0.75 m
c) 1.0 m
d) 1.5 m
Ans: b
87. A ball is dropped from a height of 16 m on a horizontal floor. If it rebounds to a height of 9 m after striking the floor, the coefficient of restitution between ball and floor is
a) 1/4
b) 2/3
c) 3/4
d) 4/3
Ans: c
88. Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m/sec and 1 m/sec respectively, towards each other along the line of their centres. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is
a) 2/3
b) 1/5
c) 3/5
d) 1/3
Ans: b
89. When a body slides down an inclined surface, the acceleration of the body is given by
a) g
b) gsinG
c) g cos 6
d) g tan 6
where ‘g’ is acceleration due to gravity and 9 is the angle of inclination of surface with the horizontal.
Ans: b
90. A body is dropped from a height of 100 m and at the same time another body is projected vertically upward with a velocity of 10 m/sec. The two particles will
a) never meet
b) meet after 1 sec
c) meet after 5 sec
d) meet after 10 sec
Ans: d
91. A shell travelling with a horizontal velocity of 100 m/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan”1 x, where x is
a) 3/4
b) 4/5
c) 5/3
d) 3/5
Ans: d
92. A car goes round a curve of radius 100 m at 25 m/sec. The angle to the horizontal at which the road must be banked to prevent sideways friction on the car wheels is tan”1 x, where x is (Assume g = 10 m/sec2)
a) 3/8
b) 1/2
c) 9/5
d) 5/8
Ans: d
93. A shell of mass 100 kg travelling with a velocity of 10 m/sec breaks into two equal pieces during an explosion which provides an extra kinetic energy of 20000 Joules. If the pieces continue to move in the same direction as before, then the speed of the faster one must be
a) 20 m/sec
b) 30 m/sec
c) 40 m/sec
d) 50 m/sec
Ans: b
94. If a flywheel increases its speed from 10 rpm to 20 rpm in 10 seconds, then its angular acceleration is
a) 3.14 rad/sec 10
b) 3.14 rad/sec 20
c) 3.14 rad/sec 30
d) none of the above
Ans: c
95. Two objects moving with uniform speeds are 5 m apart after 1 second when they move towards each other and are 1 m apart when they move in the same direction. The speeds of the objects are
a) 2 m/sec and 2 m/sec
b) 3 m/sec and 2 m/sec
c) 3 m/sec and 3 m/sec
d) 4 m/sec and 6 m/sec
Ans: b
96. The angular speed of a car taking a circular turn of radius 100 m at 36 km/hr will be
a) 0.1 rad/sec
b) 1 rad/sec
c) 10 rad/sec
d) 100 rad/sec
Ans: a
97. A bullet weighing 10 gm moves with a velocity of lkm/sec. Its kinetic energy is
i) 5000 N.m
ii) 5000 kg.m
iii) 5000 J
The correct answer is
a) only (ii)
b) both (i) and (iii)
c) both (ii) and (iii)
d) all (i), (ii) and (iii)
Ans: b
98. A stone was thrown vertically upwards from the ground with a velocity of 50 m/sec. After 5 seconds another stone was thrown vertically upwards from the same place. If both the stones strike the ground at the same time, then the velocity with which the second stone was thrown should be (Assume g = 10 m/sec2)
a) 15 m/sec
b) 25 m/sec
c) 40 m/sec
d) 50 m/sec
Ans: b
99. The condilion for a lifting machine to be reversible is that its efficiency should be
a) less than 50%
b) more than 50%
c) more than 66.67%
d) equal to 100%
Ans: b
100. In a lifting machine a weight of 5 kN is lifted through 200 mm by an effort of 0.1 kN moving through 15 m. The mechanical advantage and velocity ratio of the machine are respectively
a) 50 and 75
b) 75 and 50
c) 75 and 75
d) 50 and 50
Ans: a