? ? If A=Ax i^ + Ay j^ + Az K^ B = Bx i^ + By j^ + Bz K^ then
1.?? A. B = Ax Bx + Ay By + Az Bz
2.?? A. B = Ax By + Ay Bz + Az By
3.?? A. B = Ay Bz + Az By + Az Bx
4.?? A. B = Ax Bz + Ay By + Az Bx
? The unit vector in the direction of vector A = 2 i^ -2j^ + k^ is
1.2i^ - 2j^ + k^
2.(2i^ - 2j^ +k^)/9
3.(2i^ - 2j^ +k^)/3
4.(2i^ - 2j^ +k^)/5
A body in equilibrium
1.always at rest
2.always in uniform motion
3.may be at rest or in uniform motion
4.may be at rest or in motion
A body will be in complete equilibrium when it is satisfying
1.Ist condition of equilibrium
2.2nd condition of equilibrium
3.both Ist and 2nd condition of equilibrium
4.impossible
A central force is that which
1.can produce torque
2.can not produce torque
3.some time can produce torque some time can not
4.has no relation with torque
A hoop and disc have same mass and radius. Their rotational K.E are related by an equation
1.K.Ehoop = K.Edisc
2.K.Ehoop = 2K.Edisc
3.K.Ehoop = 1/2K.Edisc
4.K.Ehoop = 4K.Edisc
A vector can be multiplied by a number. The number may be
1.dimensionless
2.dimensional scalar
3.negative
4.all a, b and c are correct
According to Einstein the gravity interaction is possible between
1.material objects only
2.material objects and electromagnetic radiation only
3.electromagnetic radiations
4.none of the above
Addition of vector obeys
1.commutative law
2.distributive law
3.associative law
4.all given laws in a , b and c
Angle between two vectors A and B can be determined by
1.their dot product
2.their cross product
3.head to tail rule
4.right hand rule
Cos?i^ + Sin?j^ is a
1.vector
2.position vector
3.vector in the direction at angle ? with x-axis
4.unit vector in the direction at angle ? with x-axis
Geo-stationary satellite completes one rotation around earth in
1.3 hours
2.6 hours
3.12 hours
4.24 hours
If A=B, which of the following is not correct?
1.A.B = A^ B^
2.|A| = |B|
3.|A^| = |B^|
4.AB^ = BA^
If east, west, north, south, up and down are representing the direction of unit vectors, then east x south has direction along
1.west
2.north
3.down
4.up
In which quadrant the two rectangular components of a vector have same sign?
1.1st
2.2nd
3.both 1st and 3rd
4.4th
In which quadrant, only value of tan will be positive?
1.first
2.second
3.third
4.both 1st and 3rd
It is easier to turn a steering wheel with both hands than with a single hand because
1.accelerating force increases on the wheel
2.two forces act on the wheel
3.two hands provide firm grip
4.couple acts on the wheel
i^ . (j^ x k^) is equal to
1.1
2.i^
3.j^
4.k^
Maximum number of components of a vector may be
1.one
2.two
3.three
4.infinite
Maximum number of rectangular components are
1.one
2.two
3.three
4.infinite
Null vector is a vector which has
1.zero magnitude
2.no specified direction
3.both a and b are correct
4.both a and b are not correct
One radian is equal to
1.67.3?
2.57.3?
3.87.3?
4.60?
Radius of geo-stationary orbit from center of earth is nearly
1.42000km
2.36000km
3.24000 km
4.18000 km
Rectangular coordinate system is also called
1.polar coordinate system
2.Cartesian coordinate system
3.cylindrical coordinate system
4.spherical coordinate system
SI unit of torque is
1.N.m
2.joule
3.both a and b are correct
4.neither a nor b is correct
The critical speed of an artificial satellite is
1.8 Kms-1
2.8.1 Kms-1
3.7.9 Kms-1
4.8 ms-1
The cross product i^ x j^ is equal to
1.zero
2.one
3.i^
4.k^
The cross product of two vectors is a negative vector when
1.they are parallel vectors
2.they are anti parallel vectors
3.they are perpendicular vector
4.they are rotated through 270?
The dimension of torque is
1.[ML2T-2]
2.[MLT-2]
3.[ML2T]
4.[ML-2T-2]
The direction of a vector in spece is specified by
1.one angle
2.two angle
3.three angle
4.no angle
The direction of linear velocity of body moving in a circle is
1.along the axis of rotation
2.along the tangent
3.directed towards the center
4.directed away form the center
The direction of vector product is given by
1.head to tail rule
2.right hand rule
3.left hand rule
4.triangular rule
The magnitude of cross product is equal to the dot product between them. The angle between the two vectors is
1.30?
2.45?
3.60?
4.180?
The magnitude of i^. (j^ x k^) is
1.0
2.1
3.-1
4.i^
The period of a circular motion is given by
1.T = rV
2.T = ?w
3.T = 2??
4.T = 2?/?
The resultant of two forces of equal magnitudes is also equal to the magnitude of the forces. The angle between the two forces is
1.30?
2.60?
3.90?
4.120?
The rotational K.E of hoop is equal to the
1.its translational K.E
2.half than its translational K.E
3.double than its translational K.E
4.four times than its translational K.E
Three coplanar forces acting on a body keep it in equilibrium. They should therefore be
1.concurrent
2.non concurrent
3.parallel
4.non parallel
Torque acting on a body determines
1.acceleration
2.linear acceleration
3.angular acceleration
4.direction of motion of the body
Torque is defined as
1.turning effect of force
2.cross product of position vector and force
3.product of force and moment arm
4.all a, b and c are correct
Two vectors A and B are making angle ? with each other. The scalar projection of vector B on vector A is written as
1.A.B/A
2.A.B/B
3.A.cos ?
4.both a and b are correct
Two vectors are A = 3i^+2j^ -k^& B = 3i^-2j^ +k^ , then
1.B is anti parallel to A
2.B is negative vector of A
3.B has negative magnitude
4.B is perpendicular to A
Unit vector n^ is along
1.x-axis
2.normal on a surface
3.y-axis
4.z-axis
What is the angle that the given vector makes with y-axis? A=2 i^+??12 j^
1.30?
2.60?
3.90?
4.120?
When a body moves in a circle, the angle between its linear velocity and angular velocity is always
1.180?
2.0?
3.90?
4.45?
which of the following pairs does not have identical dimensions ?
1.torque and energy
2.momentum and impulse
3.energy and work
4.mass and moment of inertia
Which one is a unit vector?
1.??3 i^ + ??3 j^ + ??3 k^
2.1/??3 i^ + 1/??3 j^ +1/ ??3 k^
3.??3 / 3 i^ + ??3 / 3 j^ + ??3 / 3 k^
4.both b and c are correct
Which one is not a correct relation?
1.AxB = -BxA
2.|AxB| = -|BxA|
3.AxB = AB Sin?n^
4.BxA = AB Sin?(-n^)
Which one is not a type of dynamic equilibrium?
1.rotational equilibrium
2.translational equilibrium
3.static equilibrium
4.both a and c are corret answer.
Which one is not correct for a vector A= 2??2 i^ + ??2 j^?
1.has direction ?=45? with x-axis
2.has magnitude 2
3.has magnitude 2 and direction ?=45? with y-axis
4.has magnitude -2