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Mechanics

Physics

A wire of uniform cross-section is bent in the shape shown in figure. The co-ordinate of the centre of mass of each side are shown in (figure). The coordinates of the centre of mass of the system are

A wire of uniform cross-section is bent in the shape shown in figure. The co-ordinate of the centre of mass of each side are shown in (figure). The coordinates of the centre of mass of the system are

PhysicsMechanics

Mechanics

Physics

Five uniform circular plates, each of diameter b and mass m are laid out in a pattern shown. Using the origin shown. find the y co-ordinate of the centre of mass of the five-plate system.

Five uniform circular plates, each of diameter b and mass m are laid out in a pattern shown. Using the origin shown. find the y co-ordinate of the centre of mass of the five-plate system.

PhysicsMechanics

Mechanics

Physics

A square of side a and uniform thickness is divided into four equal parts. If upper right part is removed, then find the coordinates of centre of mass of remaining part.

A square of side a and uniform thickness is divided into four equal parts. If upper right part is removed, then find the coordinates of centre of mass of remaining part.

PhysicsMechanics

Mechanics

Physics

Three particles of masses $1 kg comma 3 over 2 kg$ , and 2 kg are located the vertices of an equilateral triangle of side a. The x, y coordinates of the centre of mass are

Three particles of masses $1 kg comma 3 over 2 kg$ , and 2 kg are located the vertices of an equilateral triangle of side a. The x, y coordinates of the centre of mass are

PhysicsMechanics

Mechanics

Physics

A small body slides down a smooth uneven surface from a height H, which eventually emerges into a circular loop of radius R(<H) what should be the value of H, so the that force on the body at A is $square root of 2$ times its weight?

A small body slides down a smooth uneven surface from a height H, which eventually emerges into a circular loop of radius R(<H) what should be the value of H, so the that force on the body at A is $square root of 2$ times its weight?

PhysicsMechanics

Mechanics

Physics

A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assuming the total energy of the ball-Earth system remains constant. What is the difference of tension in string at bottom and top during circular motion $open parentheses T subscript text bolem end text end subscript minus T subscript text sop end text end subscript equals ? close parentheses$

A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assuming the total energy of the ball-Earth system remains constant. What is the difference of tension in string at bottom and top during circular motion $open parentheses T subscript text bolem end text end subscript minus T subscript text sop end text end subscript equals ? close parentheses$

PhysicsMechanics

Mechanics

Physics

A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The equation relating $alpha text and end text beta$ is

A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The equation relating $alpha text and end text beta$ is

PhysicsMechanics

Mechanics

Physics

Three identical particles each of mass 1kg are placed with their centres on a straight line. Their centres are marked A,B and C respectively. The distance of centre of mass of the system from A is

Three identical particles each of mass 1kg are placed with their centres on a straight line. Their centres are marked A,B and C respectively. The distance of centre of mass of the system from A is

PhysicsMechanics

Mechanics

Physics

A homogeneous plate P Q R S T is as shown in figure. The centre of mass of plate lies at midpoint A of segment QT. Then the ratio of is $b over a$ $left parenthesis P space Q equals P space T equals b space semicolon space Q space R equals R space S equals S space T equals a right parenthesis$

A homogeneous plate P Q R S T is as shown in figure. The centre of mass of plate lies at midpoint A of segment QT. Then the ratio of is $b over a$ $left parenthesis P space Q equals P space T equals b space semicolon space Q space R equals R space S equals S space T equals a right parenthesis$

PhysicsMechanics

Mechanics

Physics

A small block slides with velocity $v subscript 0 equals 0.5 square root of g r end root$ on the horizontal frictionless surface as shown in the fig. The block leaves the surface at point C The angle $theta$ in the figure is:

A small block slides with velocity $v subscript 0 equals 0.5 square root of g r end root$ on the horizontal frictionless surface as shown in the fig. The block leaves the surface at point C The angle $theta$ in the figure is:

PhysicsMechanics

Mechanics

Physics

A weightless rod of length 2l carries two equal masses ‘m’, one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in horizontal position. The speed of the mass B at the instant rod, become vertical is:

A weightless rod of length 2l carries two equal masses ‘m’, one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in horizontal position. The speed of the mass B at the instant rod, become vertical is:

PhysicsMechanics

Mechanics

Physics

A stone of mass 1 kg tied to a light inextensible string of length $L equals 10 over 3 m$ is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be 10 m / sec², the speed of the stone at the highest point of the circle is

A stone of mass 1 kg tied to a light inextensible string of length $L equals 10 over 3 m$ is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be 10 m / sec², the speed of the stone at the highest point of the circle is

PhysicsMechanics

Mechanics

Physics

Three identical spheres each of radius R are placed touching each other on a horizontal table as shown in figure. The co-ordinates of centre of mass are:

Three identical spheres each of radius R are placed touching each other on a horizontal table as shown in figure. The co-ordinates of centre of mass are:

PhysicsMechanics

Mechanics

Physics

$A space m a n space left parenthesis m a s s space equals 50 space k g right parenthesis space a n d space h i s space s o n space left parenthesis m a s s space equals 20 space k g right parenthesis space a r e space s tan d i n g space o n space a space f r i c t i o n l e s s space s u r f a c e space f a c i n g space e a c h space o t h e r. space T h e space m a n space p u s h e s space h i s space s o n space s o space t h a t space h e space s t a r t s space m o v i n g space a t space a space s p e e d space o f space 0.70 space m s to the power of negative 1 end exponent space w i t h space r e s p e c t space t o space t h e space m a n. space T h e space s p e e d space o f space t h e space m a n space w i t h space r e s p e c t space t o space t h e space s u r f a c e space i s space colon$

$A space m a n space left parenthesis m a s s space equals 50 space k g right parenthesis space a n d space h i s space s o n space left parenthesis m a s s space equals 20 space k g right parenthesis space a r e space s tan d i n g space o n space a space f r i c t i o n l e s s space s u r f a c e space f a c i n g space e a c h space o t h e r. space T h e space m a n space p u s h e s space h i s space s o n space s o space t h a t space h e space s t a r t s space m o v i n g space a t space a space s p e e d space o f space 0.70 space m s to the power of negative 1 end exponent space w i t h space r e s p e c t space t o space t h e space m a n. space T h e space s p e e d space o f space t h e space m a n space w i t h space r e s p e c t space t o space t h e space s u r f a c e space i s space colon$

PhysicsMechanics

Mechanics

Physics

$T h e space t r a j e c t o r y space o f space a space p r o j e c t i l e space n e a r space t h e space s u r f a c e space o f space t h e space e a r t h space i s space g i v e n space a s space y equals 2 space x minus 9 space x squared. space I f space i t space w e r e space l a u n c h e d space a t space a n space a n g l e space theta subscript 0 space w i t h space s p e e d space v subscript 0 space t h e n space left parenthesis g equals 10 space m space s to the power of negative 2 end exponent right parenthesis colon$

$T h e space t r a j e c t o r y space o f space a space p r o j e c t i l e space n e a r space t h e space s u r f a c e space o f space t h e space e a r t h space i s space g i v e n space a s space y equals 2 space x minus 9 space x squared. space I f space i t space w e r e space l a u n c h e d space a t space a n space a n g l e space theta subscript 0 space w i t h space s p e e d space v subscript 0 space t h e n space left parenthesis g equals 10 space m space s to the power of negative 2 end exponent right parenthesis colon$

PhysicsMechanics

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