Question

A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up a plane of inclination with acceleration a0 is

## The correct answer is:

### Related Questions to study

In the situation shown in figure all the string are light and inextensible and pullies are light. There is no friction at any surface and all block are of cuboidal shape. A horizontal force of magnitude F is applied to right most free end of string in both cases of figure 1 and figure 2 as shown. At the instant shown, the tension in all strings are non zero. Let the magnitude of acceleration of large blocks (of mass M) in figure 1 and figure 2 are and respectively. Then:

In the situation shown in figure all the string are light and inextensible and pullies are light. There is no friction at any surface and all block are of cuboidal shape. A horizontal force of magnitude F is applied to right most free end of string in both cases of figure 1 and figure 2 as shown. At the instant shown, the tension in all strings are non zero. Let the magnitude of acceleration of large blocks (of mass M) in figure 1 and figure 2 are and respectively. Then:

A plank is held at an angle to the horizontal (Fig.) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. Acceleration and direction in which a man of mass m should move so that the plank does not move.

A plank is held at an angle to the horizontal (Fig.) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. Acceleration and direction in which a man of mass m should move so that the plank does not move.

A block of mass m1 lies on top of fixed wedge as shown in figure-1 and another block of mass m2 lies on top of wedge which is free to move as shown in figure-2. At time t = 0, both the blocks are released from rest from a vertical height h above the respective horizontal surface on which the wedge is placed as shown. There is no frcition between block and wedge in both the figures. Let T1 and T2 be the time taken by block in figure-1 and block in figure-2 respectively to just reach the horizontal surface, then :

A block of mass m1 lies on top of fixed wedge as shown in figure-1 and another block of mass m2 lies on top of wedge which is free to move as shown in figure-2. At time t = 0, both the blocks are released from rest from a vertical height h above the respective horizontal surface on which the wedge is placed as shown. There is no frcition between block and wedge in both the figures. Let T1 and T2 be the time taken by block in figure-1 and block in figure-2 respectively to just reach the horizontal surface, then :

System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is –

System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is –

### Let , then which of the following is true?

### Let , then which of the following is true?

### For all twice differentiable functios , with

### For all twice differentiable functios , with

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle should be :–

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle should be :–

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–

### Let be a twice differentiable function on . If , and , for all , then

### Let be a twice differentiable function on . If , and , for all , then

A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of is given :

A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of is given :

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration, . If the coefficient of friction between the rod and bead is , and gravity is neglected, then the time after which the bead starts slipping is

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration, . If the coefficient of friction between the rod and bead is , and gravity is neglected, then the time after which the bead starts slipping is

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction and the distance x(=QR), are, respectively close to:

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction and the distance x(=QR), are, respectively close to:

### An observer can see through a pin–hole the top end of a thin rod of height *h*, placed as shown in the figure. The beaker height is 3*h* and its radius *h*. When the beaker is filled with a liquid up to a height 2*h*, he can see the lower end of the rod. Then the refractive index of the liquid is

=

### An observer can see through a pin–hole the top end of a thin rod of height *h*, placed as shown in the figure. The beaker height is 3*h* and its radius *h*. When the beaker is filled with a liquid up to a height 2*h*, he can see the lower end of the rod. Then the refractive index of the liquid is

=

### A diverging beam of light from a point source *S* having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is *t* and the refractive index *n*, then the divergence angle of the emergent beam is

### A diverging beam of light from a point source *S* having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is *t* and the refractive index *n*, then the divergence angle of the emergent beam is

### A rectangular glass slab *ABCD*, of refractive index *n*_{1}, is immersed in water of refractive index A ray of light in incident at the surface *AB* of the slab as shown. The maximum value of the angle of incidence *a*_{max}, such that the ray comes out only from the other surface *CD* is given by

_{max}

### A rectangular glass slab *ABCD*, of refractive index *n*_{1}, is immersed in water of refractive index A ray of light in incident at the surface *AB* of the slab as shown. The maximum value of the angle of incidence *a*_{max}, such that the ray comes out only from the other surface *CD* is given by

_{max}