A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between:
1. 14 m/s and 15 m/s
2. 15 m/s and 16 m/s
3. 16 m/s and 17 m/s
4. 13 m/s and 14 m/s
As shown in the figure, two masses of \(10~\text{kg}\) and \(20~\text{kg}\), respectively are connected by a massless spring. A force of \(200~\text{N}\) acts on the \(20~\text{kg}\) mass. At the instant shown, the \(10~\text{kg}\) mass has an acceleration of \(12~\text{m/s}^2\) towards the right. The acceleration of \(20~\text{kg}\) mass at this instant is:
1. \(12~\text{m/s}^2\)
2. \(4~\text{m/s}^2\)
3. \(10~\text{m/s}^2\)
4. zero
A point mass '\(m\)' is moved in a vertical circle of radius 'r' with the help of a string. The velocity of the mass is \(\sqrt{7 g r} \) at the lowest point.
The tension in the string at the lowest point will be:
1. \(6mg\)
2. \(7mg\)
3. \(8mg\)
4. \(mg\)
A particle of mass ‘m’ having speed v goes in a vertical circular motion such that its centre is at its origin, as shown in the figure. If at any instant the angle made by the string with a negative y-axis is then the tension in the string is:
[Take radius = R]
Three blocks A, B and C of mass 3M, 2M and M respectively are suspended vertically with the help of springs PQ and TU and a string RS as shown in fig. The acceleration of blocks A, B and C are respectively.
The value of acceleration \(a_{1}\) at the moment string RS is cut will be:
1. g downward
2. g upward
3. more than g downward
4. zero
If between block A and inclined plane is 0.5 and that between block B and the inclined plane is 0.8, then the normal reaction between blocks A and B will be:
1. 180 N
2. 216 N
3. 0
4. None of these
Calculate the reading of the spring balance shown in the figure: (take \(g=10\) m/s2)
1. \(60\) N
2. \(40\) N
3. \(50\) N
4. \(80\) N
A metal sphere is suspended from a wall by a string. The forces acting on the sphere are shown in the figure. Which of the following statements is NOT correct?
1. |
\(\vec N+\vec T+\vec W=0\) |
2. | \(T^2=N^2+W^2\) |
3. | \(T = N + W\) | 4. | \(N = W \tan \theta\) |
The angle of banking for a cyclist taking a turn at a curve is given by tan where symbols have their usual meaning. The value of n is:
1. | 1
|
2. | 2
|
3. | 3
|
4. | 4 |
A body of mass m is moving on a concave bridge ABC of the radius of curvature R at a speed v. The normal reaction of the bridge on the body at the instant it is at the lowest point of the bridge is:
1.
2.
3. mg
4.