Home
Class 11
PHYSICS
Suppose the bob of the previous problem ...

Suppose the bob of the previous problem has a speed of 1.4 m/s when the string makes an angle of 0.20 radian with the vertical. Find the tension at this instant. You can use `costheta=1-theta^2/2 and sintheta=theta` for small theta`.

Text Solution

Verified by Experts

The correct Answer is:
A
Bob has a veloicyt `1.4 m/sec,` when the string makes and angle of 0.2 radian,
`g0.1 kg, m=100`
`r=1m,v=1.4m/sec`

From the diagram,
`T-mgcostheta=(mv^2)/R`
`rarr T=(mv^2)/r+mgcostheta`
Given `costheta=1/theta^2/2` for small theta`
`:. T=(0.1xx(1.4)^2)/1+(0.1)xx9.8(1-theta^2/2)`
`=0.196+0.98xx(1-2^2/2)`
`=0.196+0.98xx(0.98)`
`0.196+0.9604`
`=1.156N~~1.16N`
Promotional Banner

Similar Questions

Explore conceptually related problems

If sintheta+costheta=1 , then the value of sin(2theta) is

The bob of a simple pendulum of length 1 m has mass 100g and a speed of 1.4 m/ s at the lowest point in its path. Find the tension in the string at this moment. Take g=9.8 m//sec^(2) (AS_(1))

If sin theta_1 + sintheta_2 + sin theta_3=3, then find the value of cos theta_1 + cos theta_2 + cos theta_3.

A bullet of mass M is fired with a velocity 50m//s at an angle with the horizontal. At the highest point of its trajectory, it collides head-on with a bob of mass 3M suspended by a massless string of length 10//3 metres and gets embeded in the bob. After the collision, the string moves through an angle of 120^@ . Find (i) the angle theta , (ii) the vertical and horizontal coordinates of the initial position of the bob with respect to the point of firing of the bullet. Take g=10 m//s^2

If 0 lt theta lt (pi)/2 and 5 tan theta = 4 then (5 sin theta - 3 cos theta) / (sintheta +2 cos theta ) = 5/14

A simple pendulum of length 40 cm oscillates with an angular amplitude of 0.04 rad. Find a. the time period b. the linear amplitude of the bob, c. The speed of the bob when the strig makes 0.02 rad with the vertical and d. the angular acceleration when the bob is in moemntary rest. Take g=10 ms^-2 .

The block A is moving downward with constant velocity v_(0.) Find the velocity of the block B. When the string makes an angle theta with the horizontal

If 2tan^(-1)(costheta)=tan^(-1)(2cosectheta) , then show that theta=pi/4 .

Find the most general value of theta satisfying the equation tantheta=-1 and costheta=(1)/(sqrt(2)) .

A simple pendulum of time period 1s and length l is hung from a fixed support at 0. Such that the bob is at a distance H vertically above A on the ground (figure) the amplitude is theta_(0) the string snaps at theta =(theta_0)/(2) . Find the time taken by the bob to hit the ground. Also find distance from A where bob hits the ground. Assume theta_(0) to be small, so that sin theta_(0) approx theta_(0)" and"cos theta_(0) approx 1 . .