Physics
Mechanics
Easy

Question

The minimum height of the obstacle so that the sphere can stay in equilibrium is (R is radius of the sphere)

  1. fraction numerator R over denominator 1 plus sin invisible function application theta end fraction
  2. fraction numerator R over denominator 1 plus cos invisible function application theta end fraction
  3. R left parenthesis 1 minus sin invisible function application theta right parenthesis
  4. R left parenthesis 1 minus cos invisible function application theta right parenthesis

The correct answer is: R left parenthesis 1 minus cos invisible function application theta right parenthesis


    text  If  end text theta text  is angle between direction of  end text mg text  and normal to incline passing through centre of sphere,  end text
cos invisible function application theta equals open parentheses fraction numerator R minus h over denominator R end fraction close parentheses

    Related Questions to study

    Mechanics
    Physics

    A space c y l i n d e r space r e s t s space o n space a space h o r i z o n t a l space r o t a t i n g space d i s c space a s space s h o w n. space D i s tan c e space b e t w e e n space t h e space a x e s space o f space t h e space d i s c space
text  and cylinder is  end text straight R text  . Coefficient of friction between disc and cylinder is  end text mu greater than D over h. text  Where  end text D equals 2 r text  is  end text
text  diameter of cylinder. Value of  end text omega text  such that cylinder falls off the disc will be  end text

    A space c y l i n d e r space r e s t s space o n space a space h o r i z o n t a l space r o t a t i n g space d i s c space a s space s h o w n. space D i s tan c e space b e t w e e n space t h e space a x e s space o f space t h e space d i s c space
text  and cylinder is  end text straight R text  . Coefficient of friction between disc and cylinder is  end text mu greater than D over h. text  Where  end text D equals 2 r text  is  end text
text  diameter of cylinder. Value of  end text omega text  such that cylinder falls off the disc will be  end text

    PhysicsMechanics
    Mechanics
    Physics

    The maximum ratio of b/h for which the homogeneous block will slide without toppling under the action of force F. Coefficient of static friction between the block and incline is mu.

    The maximum ratio of b/h for which the homogeneous block will slide without toppling under the action of force F. Coefficient of static friction between the block and incline is mu.

    PhysicsMechanics
    Mechanics
    Physics

    A horizontal force F is applied at the top of an equilateral triangular block of mass m and side L as shown. The minimum value of coefficient of friction between block and the horizontal surface to topple the block before it slides.

    A horizontal force F is applied at the top of an equilateral triangular block of mass m and side L as shown. The minimum value of coefficient of friction between block and the horizontal surface to topple the block before it slides.

    PhysicsMechanics
    parallel
    Mechanics
    Physics

    A horizontal force F is applied to a rectangular block of mass m width b and height H so that block moves with constant velocity.  is coefficient of kinetic friction. If F is applied at a height H/2 as shown, value of x where line of action of resultant contact force applied by the surface on the block acts.

    A horizontal force F is applied to a rectangular block of mass m width b and height H so that block moves with constant velocity.  is coefficient of kinetic friction. If F is applied at a height H/2 as shown, value of x where line of action of resultant contact force applied by the surface on the block acts.

    PhysicsMechanics
    Mechanics
    Physics

    A cubical block of mass m and edge length L is sliding down on an inclined plane with uniform velocity. Torque due to the normal force applied by the incline on the block about its centre of mass is

    A cubical block of mass m and edge length L is sliding down on an inclined plane with uniform velocity. Torque due to the normal force applied by the incline on the block about its centre of mass is

    PhysicsMechanics
    Mechanics
    Physics

    An isosceles right triangular plate ABC of mass m is free to rotate in vertical plane about a fixed horizontal axis through A. It is supported by a string such that the side AB is horizontal. The reaction at the support A is

    An isosceles right triangular plate ABC of mass m is free to rotate in vertical plane about a fixed horizontal axis through A. It is supported by a string such that the side AB is horizontal. The reaction at the support A is

    PhysicsMechanics
    parallel
    Mechanics
    Physics

    In the above case rod does not slip until theta equals

    In the above case rod does not slip until theta equals

    PhysicsMechanics
    Mechanics
    Physics

    A rod of mass m and length L is released from rest from vertical position as shown. The normal force exerted on the rod by ground as function of  as rod falls downward without slip

    A rod of mass m and length L is released from rest from vertical position as shown. The normal force exerted on the rod by ground as function of  as rod falls downward without slip

    PhysicsMechanics
    Mechanics
    Physics

    text  In the above situation of  end text mu text  is coefficient of friction between the rod and the surface  end text tan invisible function application theta equals

    text  In the above situation of  end text mu text  is coefficient of friction between the rod and the surface  end text tan invisible function application theta equals

    PhysicsMechanics
    parallel
    Mechanics
    Physics

    One fourth length of a uniform rod of mass m and length L is placed on a rough horizontal surface and it is held stationary in horizontal position by means of a light thread as shown. The thread is then burnt and the rod starts rotating about the edge when the rod about to slide on the edge, angle made by the rod with horizontal is , then normal force on the rod applied by edge of the table is

    One fourth length of a uniform rod of mass m and length L is placed on a rough horizontal surface and it is held stationary in horizontal position by means of a light thread as shown. The thread is then burnt and the rod starts rotating about the edge when the rod about to slide on the edge, angle made by the rod with horizontal is , then normal force on the rod applied by edge of the table is

    PhysicsMechanics
    Mechanics
    Physics

    A uniform thin rod of mass m and length L is standing on a smooth horizontal surface. A slight disturbance causes the lower end to slip on the smooth surface and the rod starts falling. Then velocity of centre of mass of the rod when it makes an angle theta equals 45 to the power of o  with horizontal is

    A uniform thin rod of mass m and length L is standing on a smooth horizontal surface. A slight disturbance causes the lower end to slip on the smooth surface and the rod starts falling. Then velocity of centre of mass of the rod when it makes an angle theta equals 45 to the power of o  with horizontal is

    PhysicsMechanics
    Mechanics
    Physics

    A uniform rod of mass m and length L is smoothly pivoted at one of its ends. When it is released from rest from horizontal position, it swings in a vertical circle. When the rod swings through an angle  theta with horizontal, reaction force offered by the rod along normal and tangential directions are respectively

    A uniform rod of mass m and length L is smoothly pivoted at one of its ends. When it is released from rest from horizontal position, it swings in a vertical circle. When the rod swings through an angle  theta with horizontal, reaction force offered by the rod along normal and tangential directions are respectively

    PhysicsMechanics
    parallel
    Mechanics
    Physics

    Consider the situation as shown in the diagram. The pulley has radius R and moment of inertia I. The block is released when the spring (spring constant K) is unstretched. Find the speed of block when the block has fallen a distance h. Assume no slipping.

    Consider the situation as shown in the diagram. The pulley has radius R and moment of inertia I. The block is released when the spring (spring constant K) is unstretched. Find the speed of block when the block has fallen a distance h. Assume no slipping.

    PhysicsMechanics
    Mechanics
    Physics

    A uniform circular disc has radius R and mass m. A particle also of mass m is fixed at a point A on the edge of the disc as shown in the figure. The disc can rotate freely about a fixed horizontal chord P Q that is at a distance R/4 from the center C of the disc. The line AC is perpendicular of P Q. Initially, the disc is held vertical with the point A at its highest position. It is then allowed to fall so that it starts rotating about P Q. Find the linear speed of the particle as it reaches its lowest position.

    A uniform circular disc has radius R and mass m. A particle also of mass m is fixed at a point A on the edge of the disc as shown in the figure. The disc can rotate freely about a fixed horizontal chord P Q that is at a distance R/4 from the center C of the disc. The line AC is perpendicular of P Q. Initially, the disc is held vertical with the point A at its highest position. It is then allowed to fall so that it starts rotating about P Q. Find the linear speed of the particle as it reaches its lowest position.

    PhysicsMechanics
    Mechanics
    Physics

    A particle of mass m is released from rest at point A which falls parallel to the vertical direction. Angular momentum of that particle as function of time t with respect to origin o is

    A particle of mass m is released from rest at point A which falls parallel to the vertical direction. Angular momentum of that particle as function of time t with respect to origin o is

    PhysicsMechanics
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.