Home
Class 11
PHYSICS
A carpenter has constructed a toy as sho...

A carpenter has constructed a toy as shown in figure. If the density of the material of the sphere is 12 tirnes that of cone, the `y-` coordinate of `COM` of toy point `O`

A

`3R`

B

`(9R)/(2)`

C

`(7R)/(2)`

D

`4R`

Text Solution

Verified by Experts

The correct Answer is:
D

Mass of cone `M_(1)=rho((1)/(3) pi (2R^(2))4R)`
`c=(rho)/(3)pi (16R^(3))`
mass of sphere `M_(2)`
`=12rho((4)/(3)piR^(3))=rhi16pi(R^(3))`
`y_(1)=y_(com)(Co n e)=(H)/(4)=(4R)/(4)=R`
`y_(2)=y_(com)(sphere)=4R+R=5R`
`y_(com)(t o y)=(M_(1)y_(1)+M_(2)y_(2))/(M_(1)+M_(2))`
`=(16rhopiR^(3))/(3)(R)+16rhopi(R^(3))5R`
`16pi rhoR^(3)[(1)/(3)+1]`
`rArr (16 rho pi R^(3)[(R)/(3)+5R])/(16rho phi R^(3)[(1)/(3)+1])=4R`
Promotional Banner

Topper's Solved these Questions

  • DAILY PRACTICE PROBLEMS

    RESONANCE|Exercise dpp 80|4 Videos

  • DAILY PRACTICE PROBLEMS

    RESONANCE|Exercise dpp 81|4 Videos

  • DAILY PRACTICE PROBLEMS

    RESONANCE|Exercise dpp 78|3 Videos

  • CURRENT ELECTRICITY

    RESONANCE|Exercise Exercise|54 Videos

  • ELASTICITY AND VISCOCITY

    RESONANCE|Exercise Advanced Level Problems|9 Videos

Similar Questions

Explore conceptually related problems

A carpenter has constructed a toy as shown in the figure. If the density of a material of the sphere is 12 times that of cone, the position of the centre of mass of the toy is given by : .

Three resistance are joined together to form a letter Y, as shown in figure. If the potentials of the terminals A, B and C are 6V, 3V and 2V respectively, then the potential of the point O will be

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in figure. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical partition has a diameter of 5 cm, while the base diameter of the cylindrical protion is 3 cm.Find the slant height of conical portion.

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in figure. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical partition has a diameter of 5 cm, while the base diameter of the cylindrical protion is 3 cm. If the conical portion is to be painted orange, find the area to be painted orange. Find the area of the rockeeet peainted with each of these colours? (Take pi = 3.14)

In figure-I is shown a sphere of mass m and radius r resting at the bottom of a large container filled with water. Depth of the container is h . Density of material of the sphere is the same as that of water. Now hte whole sphere is slowly pulled out of water as shown in figure-II Work done by the agent in pulling the sphere is equal to

A solid wooden cone has been supported by a string inside water as shown in the figure. The radius of the circular base of the cone is R and the volume of the cone is V . In equilibrium the base of the cone is at a depth H below the water surface. Density of wood is d (lt rho , density of water) Then tension in the string is

A solid wooden cone has been supported by a string inside water as shown in the figure. The radius of the circular base of the cone is R and the volume of the cone is v. In equilibrium the base of the cone is at a depth H below the water surface. Density of wood is d( ltrho , density of water). (a) Find tension in the string. (b) Find the force applied by the water on the slant surface of the coone. take atmospheric pressure to be p_(0) .

A disc (of radius r cm) of uniform thickness and uniform density sigma has a square hole with sides of length l = (r )/(sqrt(2)) cm . One corner of the hole is located at the centre of the disc and centre of the hole lies y-axis as shown. Then the y-coordinate of position of centre of mass of disc with hole (in cm) is. .

A wooden toy rocket is in the shape of a cone mounted on a cylinder as shown in Fig. 16.36. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take pi=3. 14 )

The variation of temprature of a material as heat is given to it at a constant rate is shown in the figure. The material is in solid state at the point O. The state of the material at the point P is…..