MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Work Done by Force of Gravity

Two blocks of...

Question

Two blocks of mass $m_{1}$ = 10kg and $m_{2}$ = 5kg connected to each other by a massless inextensible string of length 0.3m are placed along a diameter of a turntable. The coefficient of friction between the table and $m_{1}$ is 0.5 while there is no friction between $m_{2}$ and the table. The table is rotating with an angular velocity of 10rad/sec about a vertical axis passing through its center. The masses are placed along the diameter of the table on either side of the center O such that $m_{1}$ is at a distance of 0.124 m from O. the masses are observed to be at rest with respect to an observer on the turntable.
(i) Calculate the frictional force on $m_{1}$
(ii) What should be the minimum angular speed of the turntable so that the masses will slip from this position?

Open in App

Solution

$m_{1} = 10 k g, m_{2} = 5 k g, l = 0.3 m, l = l + l_{1} + l_{2}, μ_{1} =$ coefficient of friction between table and $m_{1} = 0.5, w = 10 r a d / s, l_{1} = 0.124 m$
$(i)$ Centrifugal force acting on $m_{1}$ :
$F_{1} = m_{1} w^{2} l_{1}$
Centrifugal force acting on $m_{2}$
$F_{2} = m_{2} w^{2} (l - l_{1})$
The frictional force on $m_{1}$ is equal to the difference of these:
$f = | F_{2} - F_{1} | = w^{2} | m_{2} (l - l_{1}) - m_{1} l_{1} | = {(10)}^{2} | 5 \times (0.3 - 0.124) - 10 \times 0.124 | = 36 N$

$(i i)$ If the masses start to slip, $f$ should be equal to kinetic friction:
$f = | F_{2} - F_{1} | = w^{2} | m_{2} (l - l_{1}) - m_{1} l_{1} | = {(10)}^{2} | 5 \times (0.3 - 0.124) - 10 \times 0.124 | = 36 N$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Two blocks of mass

m_{1} = 10 k g a n d m_{2} = 5 k g

connected to each other by a massless inextensible string of length

0.3

m are placed along a diameter of turn table. The coefficient of friction between the table and

m_{1} i s 0.5

while there is no friction between

m_{2}

and the table. The table is rotating with an angular velocity

10

radian see about a vertical axis passing through its centre O. The masses are placed along a diameter of the table on either side of the centre O such that the mass m1 is at a distance of

0.124

m from O. The masses are observed to be at rest with rest with respect to an observer on the turn table.
Calculate the frictional force on

m_{1}

:

Q. Two blocks of masses

m_{1} = 10 kg

m_{2} = 5 kg

connected to each other by a massless inextensible string of length

0.3 m

are placed along a diameter of a turn table. The coefficient of static friction between the table and block

m_{1}

μ = 0.5

while there is no friction between block

m_{2}

and the table. The table is rotating with an angular speed of

10 rad/s

about a vertical axis passing through its centre

O

. The masses are placed along the diameter of turn table on either side of the centre

O

such that the mass

m_{1}

is at a distance of

0.124 m

O

. The masses are observed to be rotating with the turn table without slipping. Calculate the frictional force acting on block

m_{1}

.

Q. Two blocks of masses

m_{1} = 10 kg

m_{2} = 5 kg

connected to each other by a massless inextensible string of length

0.3 m

are placed along a diameter of a turn table. The coefficient of static friction between the table and block

m_{1}

μ = 0.5

,while there is no friction between block

m_{2}

and the table. The table is rotating with an angular speed of

10 rad/s

about a vertical axis passing through its centre

O

. The masses are placed along the diameter of turn table on either side of the centre

O

such that the mass

m_{1}

is at a distance of

0.124 m

O

. The masses are observed to be rotating with the turn table without slipping. Calculate the frictional force acting on block

m_{1}

.

Q. There are two blocks of masses

m_{1}

m_{2}

m_{2}

on a table which is rotating with an angular velocity

ω

about the vertical axis. The coefficients of friction between the blocks is

μ_{1}

m_{2}

μ_{2} (μ_{1} < μ_{2})

. If the blocks are placed at distance R from the axis of rotation, for relative sliding between the surfaces in contact, find the:
a. Frictional force at the contacting surface
b. maximum angular speed

ω

.

m_{1}

m_{2}

are connected with a string passing over a frictionless pully fixed at the corner of the table as shown in the figure, The coefficient of static friction of mass

m_{1}

with the table is

μ s

. Calculate the minimum mass

m_{3}

that may be placed on

m_{1}

to prevent it from sliding. Check if

m_{1} = 15

m_{2} = 10

m_{3} = 25

μ_{s} = 0.2

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Work done by the force of gravity

PHYSICS

Watch in App

explore_more_icon

Explore more

Work Done by Force of Gravity

Standard X Physics

Join BYJU'S Learning Program

CrossIcon