Physics-
General
Easy

Question

Centre of mass of two uniform rods of same length but made up of different materials & kept as shown, if the meeting point is the origin of co–ordinates

  1. (L/2,L/2)    
  2. (2L/3,L/2)    
  3. (L/3,L/3)    
  4. (L/3,L/6)    

The correct answer is: (L/3,L/3)

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Statement I : The inverse of the matrix  open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets does not exist.
Statement II : The matrix  open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets is singular. [because open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 3 5 row 2 6 10 row 9 8 7 end table close vertical bar = 0, since R2 = 2R1]

Statement I : The inverse of the matrix  open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets does not exist.
Statement II : The matrix  open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 1 3 5 row 2 6 10 row 9 8 7 end table close square brackets is singular. [because open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 3 5 row 2 6 10 row 9 8 7 end table close vertical bar = 0, since R2 = 2R1]

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Two blocks A and B of masses m and 2m respectively are connected by a spring of spring constant k. The masses are moving to the right with a uniform velocity v subscript 0 end subscript each, the heavier mass leading the lighter one. The spring is of natural length during this motion. Block B collides head on with a third block C of mass 2m. at rest, the collision being completely inelastic. The maximum compression of the spring after collision is –

Two blocks A and B of masses m and 2m respectively are connected by a spring of spring constant k. The masses are moving to the right with a uniform velocity v subscript 0 end subscript each, the heavier mass leading the lighter one. The spring is of natural length during this motion. Block B collides head on with a third block C of mass 2m. at rest, the collision being completely inelastic. The maximum compression of the spring after collision is –

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Two blocks A and B of masses m and 2m respectively are connected by a spring of spring constant k. The masses are moving to the right with a uniform velocity v subscript 0 end subscript each, the heavier mass leading the lighter one. The spring is of natural length during this motion. Block B collides head on with a third block C of mass 2m. at rest, the collision being completely inelastic. The velocity of centre of mass of system of block A, B & C is-

Two blocks A and B of masses m and 2m respectively are connected by a spring of spring constant k. The masses are moving to the right with a uniform velocity v subscript 0 end subscript each, the heavier mass leading the lighter one. The spring is of natural length during this motion. Block B collides head on with a third block C of mass 2m. at rest, the collision being completely inelastic. The velocity of centre of mass of system of block A, B & C is-

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Two blocks A and B of masses m and 2m respectively are connected by a spring of spring constant k. The masses are moving to the right with a uniform velocity v subscript 0 end subscript each, the heavier mass leading the lighter one. The spring is of natural length during this motion. Block B collides head on with a third block C of mass 2m. at rest, the collision being completely inelastic. The velocity of block B just after collision is-

Two blocks A and B of masses m and 2m respectively are connected by a spring of spring constant k. The masses are moving to the right with a uniform velocity v subscript 0 end subscript each, the heavier mass leading the lighter one. The spring is of natural length during this motion. Block B collides head on with a third block C of mass 2m. at rest, the collision being completely inelastic. The velocity of block B just after collision is-

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Two blocks A and B are joined together with a compressed spring. When the system is released, the two blocks appear to be moving with unequal speeds in the opposite directions as shown in figure. Select incorrect statement(s)

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Statement I : The order of the matrix A is 4 × 5 and that of B is 3 × 4. Then the matrix AB is not possible.
Statement II : AB is defined if number of columns of A = number of rows of B

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined. If AB and BA are both defined, it is not necessary that AB = BA.

Statement I : The order of the matrix A is 4 × 5 and that of B is 3 × 4. Then the matrix AB is not possible.
Statement II : AB is defined if number of columns of A = number of rows of B

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The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined. If AB and BA are both defined, it is not necessary that AB = BA.

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A spring lies along an x axis attached to a wall at one end and a block at the other end. The block rests on a frictionless surface at x = 0. A force of constant magnitude F is applied to the block that begins to compress the spring, until the block comes to a maximum displacement X subscript m a x end subscript During the first half of the motion, applied force transfers more energy to the

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A spring lies along an x axis attached to a wall at one end and a block at the other end. The block rests on a frictionless surface at x = 0. A force of constant magnitude F is applied to the block that begins to compress the spring, until the block comes to a maximum displacement X subscript m a x end subscript . During the displacement, which of the curves shown in the graph best represents the kinetic energy of the block?

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STATEMENT-1 : One end of ideal massless spring is connected to fixed vertical wall and other end to a block of mass m initially at rest on smooth horizontal surface. The spring is initially in natural length. Now a horizontal force F acts on block as shown. Then the maximum extension in spring is equal to maximum compression in spring.

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STATEMENT-1 : One end of ideal massless spring is connected to fixed vertical wall and other end to a block of mass m initially at rest on smooth horizontal surface. The spring is initially in natural length. Now a horizontal force F acts on block as shown. Then the maximum extension in spring is equal to maximum compression in spring.

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Statement II : Trace of a matrix is equal to sum of its diagonal elements.

The trace has several properties that are used to prove important results in matrix algebra and its applications.
 Let and be two K X K matrices. Then,[eq8]

Statement I : Trace of matrix  A = open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell a subscript 11      a subscript 12      a subscript 13 end cell row cell a subscript 21      a subscript 22      a subscript 23 end cell row cell a subscript 31      a subscript 32      a subscript 33 end cell end table close square brackets is equal to a11 + a22 + a33
Statement II : Trace of a matrix is equal to sum of its diagonal elements.

Maths-General

The trace has several properties that are used to prove important results in matrix algebra and its applications.
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