Home
Class 11
PHYSICS
A rod of length L and mass M is acted on...

A rod of length L and mass M is acted on by two unequal forces `F_1` and `F_2 ( lt F) `as shown in the figure.

The tension in the rod at a distance y from the end A is given by

A

`F_1 (1- (y)/(L))+F_2 ((y)/(L))`

B

`F_2 (1-(y)/(L ) )+ F_1 ((Y)/(L))`

C

`(F_1 -F_2) (y)/(L)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Net force on the rod `= F_1 -F_2`
As mass of the rod is M , so acceleration of the rod is
` a=((F_1 -F_2))/(M)`
Now considering the motion of the rod [ whose mass is equal to `(m//L)`y] then the equation of motion is
` F_1 -T = (M )/(L ) y xx a`
where T is the tension in the rod at B .
`or F_1 -T =(M )/(L) y xx ((F_1-F_2)/(M))`
`or T= F_1 (1- (y)/(L ) ) +F_2 ((y)/(L ))`
second method : to calculate tension at B we can also consider the motion of the other of the rod i.e., BC . then the equation of motion will be
` T- F_2 =(M )/(L ) (l-y) xx a`
` or T =F_2 (M )/(L ) (L-y) xx ((F_1 -F_2))/(M)` ( using (i))
`or T=F_1 ( 1- (y)/(L ) )+F_2 ((y)/(L ))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LAWS OF MOTION

    MTG GUIDE|Exercise NEET CAFÉ (TOPICWISE PRACTIVE QUESTIONS) (LAW OF CONSERVATION OF LINEAR MOMENTUM AND ITS APPLICATIONS)|6 Videos

  • LAWS OF MOTION

    MTG GUIDE|Exercise NEET CAFÉ (TOPICWISE PRACTIVE QUESTIONS) (EQUILIBRIUM OF CONCURRENT FORCES)|7 Videos

  • LAWS OF MOTION

    MTG GUIDE|Exercise AIPMT /NEET (MCQ)|24 Videos

  • KINEMATICS

    MTG GUIDE|Exercise AIPMT/ NEET MCQs|31 Videos

  • MOTION OF SYSTEM OF PARTICLES AND RIGID BODY

    MTG GUIDE|Exercise AIPMT / NEET (MCQs)|37 Videos

Similar Questions

Explore conceptually related problems

A uniform metallic rod PQ of length 2 m is acted upon by two forces A and B along the directions as shown in the figure. Find the magnitude and position of the resultant normal force that acts on the rod.

A uniform rod of length l and mass m is hung from, strings of equal length from a ceiling as shown in figure. Determine the tensions in the strings?

Knowledge Check

  • A string of length L and mass M is lying on a horizontal table. A force F is applied at one of its ends. Tension in the string at a distance y from the end at which the force applied is

    A
    Zero
    B
    F
    C
    `(F(L-y))/(L)`
    D
    `(F(l-y))/(M )`

  • A string of length L and mass M is lying on a horizontal table. A force F is applied at one of its ends. Tension in the string at a distance x from the end at which force is applied is

    A
    Zero
    B
    F should be equal to the weight of A and B
    C
    F(L-x)/L
    D
    F(L-x)M

  • Two forces F_(1) " and " F_(2) are acting on a rod abc as shown in figure.

    A
    if `F_(1)=F_(2)` then `tau_(a)=tau_(b)=tau_(c)` ( for both forces)
    B
    if `F_(1)=F_(2)` then `tau_(a)=tau_(c)netau_(b)` ( for both forces)
    C
    if `F_(1)neF_(2)` then `tau_(a)netau_(b)netau_(c)` ( for both forces)
    D
    if `F_(1)neF_(2)` then `tau_(a)=tau_(c)netau_(b)` ( for both forces)

    • Similar Questions

    Explore conceptually related problems

    A 100 N uniforms rod of length 6I is supported by two forces F_1 and F_2 as shown here. What is the ratio for F_1 to F_2 ?

    A uniform rope of length of length L is pulled by a force F on a smooth surface. Find tension in the rope at a distance x from the end where force is applied.

    A homogeneous rod of length L is acted upon by two forces F_(1) and F_(2) applied to its ends and directed opposite to each other. With what force F will the rod be stretched at the cross section at a distance l from the end where F_(1) is applied?

    A rod length L and mass M is placed along the x -axis with one end at the origin, as shown in the figure above. The rod has linear mass density lamda=(2M)/(L^(2))x, where x is the distance from the origin. Which of the following gives the x -coordinate of the rod's center of mass?

    A uniform rod of length 3L and mass m is suspended from a horizontal roof by two strings of length L and 2L as shown. Then the tension in the left string of length L is :

    Home
    Profile