A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then train is-

1. Moving with constant velocity

2. In accelerated motion

3. In retarded motion

4. At rest

Tension on the string at point \(P\) is \(T\). The graph for tension \((T)\) versus \(x\) is shown in the figure. Then the string is:

A rod of length L and mass m is acted on by two unequal forces $F_1$ and $F_2\left(<F_1\right)$ as shown in the following figure

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

1. $F_1\left(1-\frac{y}{L}\right)+F_2\left(\frac{y}{L}\right)$

2. $F_2\left(1-\frac{y}{L}\right)+F_1\left(\frac{y}{L}\right)$

3. $\left(F_1-F_2\right)\frac{y}{L}$

4. None of the above

Five persons \(A,\ B,\ C,\ D\ \text{and}\ E \) are pulling a cart of mass \(100\ \text{kg}\) on a smooth surface, and the cart is moving with an acceleration \(3 \ \text{m /s} ^ 2\) in the East direction. When person \(A\) stops pulling, it moves with an acceleration \(1 \ \text{m /s}^ 2\) in the west direction. When person\(​​B\) stops pulling, it moves with an acceleration \(24 \ \text{m/s}^ 2\) in the north direction. The magnitude of the acceleration of the cart when only \(A\) and\(​​B\) pull the cart, keeping their directions the same as the old directions, is:

1. \(26 \ \text{m/s}^ 2\)
2. \(3\sqrt{71} \ \text{m/s}^ 2\) $\mathrm{}$
3. \(25 \ \text{m/s}^ 2\)
4. \(30 \ \text{m/s}^ 2\)