D Alembert's Principle

Q. A reel of mass m and radius of gyration k is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure. consider the thickness of the thread and its mass negligible in comparison with the radius r of the hub and the reel maas m. Symbol g represents the acceleration due to gravity.

The linear acceleration of the reel is

1. $\frac{g{r}^2}{r^2+k^2}$
2. $\frac{g{k}^2}{r^2+k^2}$
3. $\frac{grk}{r^2+k^2}$
4. $\frac{mg{r}^2}{r^2+k^2}$

Q. A thin string of negligible mass with one end fixed to the roof is wound around a circular disc of radius 2 m and mass, 10 kg as shown below. The disc rolls vertically down under the action of its own weight.Considering acceleration due to gravity as 10 m/s${}^2$, the tension is the string is

1. 0 N
2. 25.0 N
3. 33.3 N
4. 50 N

Q. Two weights W and 2W are supported in a vertical plane by a string and pulleys arranged as shown. Find the magnitude of the additional weight Q applied on the left which will give a downward acceleration of 0.1g to the weight W. Neglect friction and inertia of the pulleys.

1. W
2. $\frac{W}{2}$
3. $\frac{W}{4}$
4. $\frac{W}{6}$

Q. An electric lift is moving downward with an acceleration of $g/3$ . the vertical force between a passenger in the lift and its floor is equal to

1. 3/4 of the passenger's weight
2. 2/3 of the passenger's weight
3. passenger's weight
4. 4/3 of the passenger's weight

Q. A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plate. At the instant shown, edge QR is parallel to the x-axis and the body moves such that velocities of points P and R are $V_P$ and $V_R$ in the x and y directions, respectively. The magnitude of the angular velocity of the body is

1. $2V_P$
2. $\frac{V_R}{\sqrt{3}}$
3. $\frac{V_P}{\sqrt{3}}$
4. $2V_R$

Q. A lift originally moving downwards at 10 m/s is brought to rest with a constant retardation in a distance of 25 m. The force with which the feet of a passenger of mass 80 kg (take g = 9.8 m/s${}^2$) press downwards on the floor of the lift is

1. 160 N
2. 784 N
3. 944 N
4. 1000 N

Q. A reel of mass m and radius of gyration k is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure. consider the thickness of the thread and its mass negligible in comparison with the radius r of the hub and the reel maas m. Symbol g represents the acceleration due to gravity.


The tension in the thread is

1. $\frac{mg{r}^2}{(r^2+k^2)}$
2. $\frac{mgrk}{(r^2+k^2)}$
3. $\frac{mg{k}^2}{(r^2+k^2)}$
4. $\frac{mg}{(r^2+k^2)}$

Q. The one end of rope is passing over a frictionless pulley is tied with a block of weight, W as shown in figure. The co-efficient of friction between the block and the horizontal plane is $\mu$. If the other end is allowed to pull without sliding the block, the maximum pull is permitted as

1. $\frac{\mu Wsec\alpha }{(1+\mu tan\alpha )}$
2. $\frac{\mu Wsec\alpha }{(1-\mu tan\alpha )}$
3. $\frac{\mu Wcos\alpha }{(1+\mu tan\alpha )}$
4. $\frac{\mu Wcos\alpha }{(1-\mu tan\alpha )}$