Q. No.If the block is being pulled by the rope moving with speed \(v\) as shown, then the horizontal velocity of the block is:
1.
\(v\)
2.
\(v\text{cos} \theta\)
3.
\(\dfrac{v}{\text{cos} \theta}\)
4.
\(\dfrac{v}{\text{sin} \theta}\)
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. \(14~\text{m/s}~\text{and}~15~\text{m/s}\)
2. \(15~\text{m/s}~\text{and}~16~\text{m/s}\)
3. \(16~\text{m/s}~\text{and}~17~\text{m/s}\)
4. \(13~\text{m/s}~\text{and}~14~\text{m/s}\)
A ball of mass \(0.15~\text{kg}\) is dropped from a height \(10~\text{m}\), strikes the ground, and rebounds to the same height. The magnitude of impulse imparted to the ball is \((g=10 ~\text{m}/\text{s}^2)\) nearly:
| 1. | \(2.1~\text{kg-m/s}\) | 2. | \(1.4~\text{kg-m/s}\) |
| 3. | \(0~\text{kg-m/s}\) | 4. | \(4.2~\text{kg-m/s}\) |
A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of \(12\) m/s. If the mass of the ball is \(0.15\) kg, then the impulse imparted to the ball is:
(Assume linear motion of the ball.)
1. \(0.15\) N-s
2. \(3.6\) N-s
3. \(36\) N-s
4. \(0.36\) N-s
The motion of a particle of mass \(m\) is described by \(y=ut+\frac{1}{2}gt^{2}.\) The force acting on the particle is:
1. \(3mg\)
2. \(mg\)
3. \(\frac{mg}{2}\)
4. \(2mg\)
A boy pushes a box of mass \(2~\text{kg}\) with a force \(\vec{F} = (20 \hat{i} + 10 \hat{j} )~\text{N}\) on a frictionless surface. If the box was initially at rest, then the displacement along the \(x\text-\)axis after \(10~\text{s}\) is:
| 1. | \(250~\text{m}\) | 2. | \(400~\text{m}\) |
| 3. | \(500~\text{m}\) | 4. | \(750~\text{m}\) |
A car of mass \(m\) is moving on a level circular track of radius \(R\). If \(\mu_s\) represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:
| 1. | \(\sqrt{\dfrac{Rg}{\mu_s} }\) | 2. | \(\sqrt{\dfrac{mRg}{\mu_s}}\) |
| 3. | \(\sqrt{\mu_s Rg}\) | 4. | \(\sqrt{\mu_s m Rg}\) |
A \(60\) kg man pushes a \(40\) kg man by a force of \(60\) N. The \(40\) kg man has pushed the other man with a force of:
| 1. | \(40\) N | 2. | \(0\) |
| 3. | \(60\) N | 4. | \(20\) N |
If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be:
| (a) | going up with increasing speed |
| (b) | going down with increasing speed |
| (c) | going up with uniform speed |
| (d) | going down with uniform speed |
Choose the correct option:
1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. all of the above
In order to stop a car in shortest distance on a horizontal road, one should:
| 1. | apply the brakes very hard so that the wheels stop rotating. |
| 2. | apply the brakes hard enough to just prevent slipping. |
| 3. | pump the brakes (press and release). |
| 4. | shut the engine off and not apply brakes. |
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