The range of projectile (R) on an upward inclined plane is
g. cos² β/2u². sin (α + β). cos α
2u². sin (α + β). cos α/g. cos² β
g. cos² β/2u². sin (α - β). cos α
2u². sin (α - β). cos α/g. cos² β
Correct Answer :
D. 2u². sin (α - β). cos α/g. cos² β
Related Questions
A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by (where μ = tanφ = Coefficient of friction between the plane and the body.)
P = W tanα
P = W tan (α + φ)
P = W (sinα + μcosα)
P = W (cosα + μsinα)
The motion of a particle round a fixed axis is
Translatory
Rotary
Circular
Translatory as well as rotary
For any system of coplanar forces, the condition of equilibrium is that the
Algebraic sum of the horizontal components of all the forces should be zero
Algebraic sum of the vertical components of all the forces should be zero
Algebraic sum of moments of all the forces about any point should be zero
All of the above
One joule is equal to
0.1 N-m
1 N-m
10 N-m
100 N-m
The units of moment of inertia of an area are
kg-m²
m⁴
kg/m²
m³
The centre of gravity a T-section 100 mm × 150 mm × 50 mm from its bottom is
50 mm
75 mm
87.5 mm
125 mm
If n = number of members and y = number of joints, then for a perfect frame, n = ?
1/2
2/3
3/2
2/4
A heavy string attached at two ends at same horizontal level and when central dip is very small approaches the following curve
Circular arc
Parabola
Hyperbola
Elliptical
Moment of inertia of a rectangular section having width (b) and depth (d) about an axis passing through its C.G. and parallel to the width (b), is
db³/12
bd³/12
db³/36
bd³/36
A framed structure is perfect, if the number of members are __________ (2j - 3), where j is the number of joints.
Equal to
Less than
Greater than
None of these
A pair of smith's tongs is an example of the lever of
Zeroth order
First order
Second order
Third order
The Cartesian equation of trajectory is (where u = Velocity of projection, α = Angle of projection, and x, y = Co-ordinates of any point on the trajectory after t seconds.)
y = (gx²/2u² cos²α) + x. tanα
y = (gx²/2u² cos²α) - x. tanα
y = x. tanα - (gx²/2u² cos²α)
y = x. tanα + (gx²/2u² cos²α)
In the shown figure, the tension (T) in the string will be 
m₁. m₂. g/(m₁ + m₂)
2m₁. m₂. g/(m₁ + m₂)
(m₁ + m₂)/ m₁. m₂. g
(m₁ + m₂)/2m₁. m₂. g
In the equation of virtual work, following force is neglected
Reaction of any smooth surface with which the body is in contact
Reaction of a rough surface of a body which rolls on it without slipping
Reaction at a point or an axis, fixed in space, around which a body is constrained to turn
All of the above
When a person, on a bicycle, drives round a curve, he has to lean __________ to maintain equilibrium.
Inward
Outward
Towards front
Towards back
Non-coplanar non-concurrent forces are those forces which
Meet at one point, but their lines of action do not lie on the same plane
Do not meet at one point and their lines of action do not lie on the same plane
Do not meet at one point but their lines of action lie on the same plane
None of the above
For a self locking machine, the efficiency must be
Equal to 50 %
Less than 50 %
Greater than 50 %
100 %
Which of the following is the example of lever of first order?
Arm of man
Pair of scissors
Pair of clinical tongs
All of the above
The maximum efficiency of a screw jack is
(1 - sinφ)/(1 + sinφ)
(1 + sinφ)/(1 - sinφ)
(1 - tanφ)/(1 + tanφ)
(1 + tanφ)/(1 - tanφ)
A particle inside a hollow sphere of radius r, having coefficient of friction μ can rest up to height of
r/2
r/A
r/3
0.134 r
The principle of transmissibility of forces states that, when a force acts upon a body, its effect is
Same at every point on its line of action
Different at different points on its line of action
Minimum, if it acts at the centre of gravity of the body
Maximum, if it acts at the centre of gravity of the body
In ideal machines
Mechanical advantage is greater than velocity ratio
Mechanical advantage is equal to velocity ratio
Mechanical advantage is less than velocity ratio
Mechanical advantage is unity
The matter contained in a body, is called
Impulsive force
Mass
Weight
Momentum
A pendulum which executes one beat per second is known as
Simple pendulum
Compound pendulum
Torsional pendulum
Second's pendulum
If a body is acted upon by a number of coplanar non-concurrent forces, it may
Rotate about itself without moving
Move in any one direction rotating about itself
Be completely at rest
All of these
Two coplanar couples having equal and opposite moments
Balance each other
Produce a couple and an unbalanced force
Are equivalent
Cannot balance each other
The unit of force in S.I. units is
kilogram
Newton
Watt
Dyne
Which of the following is an equation of linear motion? (where, u and v = Initial and final velocity of the body, a = Acceleration of the body, and s = Displacement of the body in time t seconds.)
v = u + a.t
s = u.t + ½ a.t2
v2 = u2 + 2a.s
All of these
The periodic time (T) is given by (where, ω = Angular velocity of particle in rad/s.)
ω/2π
2π/ω
2π × ω
π/ω
The moment of inertia of a thin disc of mass m and radius r, about an axis through its centre of gravity and perpendicular to the plane of the disc is
mr2/2
mr2/4
mr2/6
mr2/8