General
Easy
Physics-

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration, . If the coefficient of friction between the rod and bead is , and gravity is neglected, then the time after which the bead starts slipping is

Physics-General

  1. infinitesimal
  2. fraction numerator 1 over denominator square root of mu alpha end root end fraction
  3. square root of mu over alpha end root
  4. fraction numerator mu over denominator square root of alpha end fraction

    Answer:The correct answer is: square root of mu over alpha end root

    Book A Free Demo

    +91

    Grade*

    Related Questions to study

    General
    physics-

    A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is 1 third  . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of  alpha is given :

    A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is 1 third  . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of  alpha is given :

    physics-General
    General
    maths-

    Let f be a twice differentiable function on left parenthesis 1 , 6 right parenthesis. If f left parenthesis 2 right parenthesis equals 8, f to the power of ´ end exponent left parenthesis 2 right parenthesis equals 5 comma f to the power of ´ end exponent left parenthesis x right parenthesis greater or equal than 1 and f to the power of ´ left parenthesis x right parenthesis greater or equal than 4, for all x element of left parenthesis 1 , 6 right parenthesis, then colon

    Let f be a twice differentiable function on left parenthesis 1 , 6 right parenthesis. If f left parenthesis 2 right parenthesis equals 8, f to the power of ´ end exponent left parenthesis 2 right parenthesis equals 5 comma f to the power of ´ end exponent left parenthesis x right parenthesis greater or equal than 1 and f to the power of ´ left parenthesis x right parenthesis greater or equal than 4, for all x element of left parenthesis 1 , 6 right parenthesis, then colon

    maths-General
    General
    physics-

    A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals mu The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction mu and the distance x(=QR), are, respectively close to:

    A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals mu The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction mu and the distance x(=QR), are, respectively close to:

    physics-General
    General
    physics-

    A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–

    A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–

    physics-General
    General
    physics-

    An observer can see through a pin–hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is

    The line of sight of the observer remains constant, making an angle of 45° with the normal.
    sin invisible function application theta equals fraction numerator h over denominator square root of h to the power of 2 end exponent plus left parenthesis 2 h right parenthesis to the power of 2 end exponent end root end fraction=fraction numerator 1 over denominator square root of 5 end fraction
    mu equals fraction numerator sin invisible function application 4 5 to the power of o end exponent over denominator sin invisible function application theta end fraction
    equals fraction numerator 1 divided by square root of 2 over denominator 1 divided by square root of 5 end fraction equals square root of open parentheses fraction numerator 5 over denominator 2 end fraction close parentheses end root

    An observer can see through a pin–hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is

    physics-General
    The line of sight of the observer remains constant, making an angle of 45° with the normal.
    sin invisible function application theta equals fraction numerator h over denominator square root of h to the power of 2 end exponent plus left parenthesis 2 h right parenthesis to the power of 2 end exponent end root end fraction=fraction numerator 1 over denominator square root of 5 end fraction
    mu equals fraction numerator sin invisible function application 4 5 to the power of o end exponent over denominator sin invisible function application theta end fraction
    equals fraction numerator 1 divided by square root of 2 over denominator 1 divided by square root of 5 end fraction equals square root of open parentheses fraction numerator 5 over denominator 2 end fraction close parentheses end root
    General
    physics-

    A diverging beam of light from a point source S having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

    Since rays after passing through the glass slab just suffer lateral displacement hence, we have angle between the emergent rays as alpha

    A diverging beam of light from a point source S having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

    physics-General
    Since rays after passing through the glass slab just suffer lateral displacement hence, we have angle between the emergent rays as alpha
    General
    physics-

    A rectangular glass slab ABCD, of refractive index n1, is immersed in water of refractive index n subscript 2 end subscript open parentheses n subscript 1 end subscript greater than n subscript 2 end subscript close parentheses A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD is given by

    A rectangular glass slab ABCD, of refractive index n1, is immersed in water of refractive index n subscript 2 end subscript open parentheses n subscript 1 end subscript greater than n subscript 2 end subscript close parentheses A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD is given by

    physics-General
    General
    physics-

    A smooth block is released at rest on a  incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-

    A smooth block is released at rest on a  incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-

    physics-General
    General
    physics-

    The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle theta should be :–

    The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle theta should be :–

    physics-General
    General
    maths-

    For all twice differentiable functios f colon R rightwards arrow R, with f left parenthesis 0 right parenthesis equals f left parenthesis 1 right parenthesis equals f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 0

    For all twice differentiable functios f colon R rightwards arrow R, with f left parenthesis 0 right parenthesis equals f left parenthesis 1 right parenthesis equals f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 0

    maths-General
    General
    maths-

    Let f left parenthesis x right parenthesis equals x c o s to the power of negative 1 end exponent invisible function application left parenthesis negative s i n invisible function application vertical line x vertical line right parenthesis comma x element of open square brackets negative fraction numerator pi over denominator 2 end fraction comma fraction numerator pi over denominator 2 end fraction close square brackets, then which of the following is true?

    Let f left parenthesis x right parenthesis equals x c o s to the power of negative 1 end exponent invisible function application left parenthesis negative s i n invisible function application vertical line x vertical line right parenthesis comma x element of open square brackets negative fraction numerator pi over denominator 2 end fraction comma fraction numerator pi over denominator 2 end fraction close square brackets, then which of the following is true?

    maths-General
    General
    physics-

    A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-

    A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-

    physics-General
    General
    physics-

    System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is –

    System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is –

    physics-General
    General
    physics-

    A block of mass m1 lies on top of fixed wedge as shown in figure-1 and another block of mass m2 lies on top of wedge which is free to move as shown in figure-2. At time t = 0, both the blocks are released from rest from a vertical height h above the respective horizontal surface on which the wedge is placed as shown. There is no frcition between block and wedge in both the figures. Let T1 and T2 be the time taken by block in figure-1 and block in figure-2 respectively to just reach the horizontal surface, then :


    A block of mass m1 lies on top of fixed wedge as shown in figure-1 and another block of mass m2 lies on top of wedge which is free to move as shown in figure-2. At time t = 0, both the blocks are released from rest from a vertical height h above the respective horizontal surface on which the wedge is placed as shown. There is no frcition between block and wedge in both the figures. Let T1 and T2 be the time taken by block in figure-1 and block in figure-2 respectively to just reach the horizontal surface, then :


    physics-General
    General
    maths-

    If the sides a, b, c of a triangle are in G.P. and largest angle exceeds the smallest by 6 0 to the power of 0 end exponent, then c o s blank B equals

    a comma b comma c are in GP
    equals succeeds b to the power of 2 end exponent equals a c equals succeeds s i n to the power of 2 end exponent B equals blank s i n blankA s i n blank C
    equals 2 s i n to the power of 2 end exponent B equals blank c o s blank left parenthesis A minus C right parenthesis minus blank c o s blank left parenthesis A plus C right parenthesis
    equals 2 left parenthesis 1 minus c o s to the power of 2 end exponent B right parenthesis equals blank c o s blank 6 0 to the power of 0 end exponent minus blank c o s blank left parenthesis 18 0 to the power of 0 end exponent minus B right parenthesis

    If the sides a, b, c of a triangle are in G.P. and largest angle exceeds the smallest by 6 0 to the power of 0 end exponent, then c o s blank B equals

    maths-General
    a comma b comma c are in GP
    equals succeeds b to the power of 2 end exponent equals a c equals succeeds s i n to the power of 2 end exponent B equals blank s i n blankA s i n blank C
    equals 2 s i n to the power of 2 end exponent B equals blank c o s blank left parenthesis A minus C right parenthesis minus blank c o s blank left parenthesis A plus C right parenthesis
    equals 2 left parenthesis 1 minus c o s to the power of 2 end exponent B right parenthesis equals blank c o s blank 6 0 to the power of 0 end exponent minus blank c o s blank left parenthesis 18 0 to the power of 0 end exponent minus B right parenthesis