Question
Suppose the entire system of the previous question is kept inside an elevator which is coming down with an acceleration a < g. Repeat parts (a) and (b).
✓
Answer
$\text{R}_1+\text{ma}-\text{mg}=0$
$\Rightarrow\text{R}_1=\text{m(g}-\text{a) = mg}-\text{ma} \ ...(\text{i})$
$\text{T}-\mu\text{R}_1=0\Rightarrow\text{T = m(mg}-\text{ma}) \ ...(\text{ii})$
Again, $\text{F}-\text{T}-\mu\text{R}_1=0$
$\Rightarrow\text{F}-\{\mu(\text{mg}-\text{ma})\}-\text{u}(\text{mg}-\text{ma})=0$
$\Rightarrow\text{F}-\mu\text{mg}+\mu\text{ma}-\mu\text{mg}+\mu\text{ma}=0$
$\Rightarrow\text{F}=2\mu\text{mg}-2\mu\text{ma}\Rightarrow\text{F}=2\mu\text{m(g}-\text{a})$
- Acceleration of the block be a1
$\text{R}_1=\text{mg}-\text{ma} \ ...(\text{i})$
$2\text{F}-\text{T}-\mu\text{R}_1-\text{ma}_1=0$
$\Rightarrow2\text{F}-\text{t}-\mu\text{mg}+\mu\text{a}-\text{ma}_1=0 \ ...(\text{ii})$
$\text{T}-\mu\text{R}_1-\text{Ma}_1=0$
$\Rightarrow\text{T}=\mu\text{R}_1+\text{Ma}_1$
$\Rightarrow\text{T}=\mu(\text{mg}-\text{ma})+\text{Ma}_1$
$\Rightarrow\text{T}=\mu\text{mg}-\mu\text{ma + Ma}_1$
Subtracting values of F & T, we get
$2(2\mu\text{m(g}-\text{a}))-2(\mu\text{mg}-\mu\text{ma}+\text{Ma}_1)\\-\mu\text{mg}+\mu\text{ma}-\mu\text{a}_1=0$
$\Rightarrow4\mu\text{mg}-4\mu\text{ma}-2\mu\text{mg}+2\mu\text{ma = ma}_1+\text{Ma}_1$
$\Rightarrow\text{a}_1=\frac{2\mu\text{m(g}-\text{a})}{\text{M + m}}$
Both blocks move with this acceleration but in opposite directions.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
How many is energy states are present in one mole of sodium vapour? Are they all filled in normal conditions? "How many 3s energy states are present in one mole of sodium vapour? Are they all filled in normal conditions?
Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x << R, find the time period of oscillation of the particle if it is released from there.
Determine the equivalent resistance of networks shown in Fig.
First a set of n equal resistors of R each are connected in series to a battery of emf E and internal resistance R. A current I is observed to flow. Then the n resistors are connected in parallel to the same battery. It is observed that the current is increased 10 times. What is 'n'?
In a series LCR circuit with an AC source, $\text{R}=300\Omega,\text{C}=20\mu\text{F},\text{L}=1.0\text{ henry},\in_0=50\text{V}$ and $\nu=\frac{50}{\pi}\text{Hz}.$ Find:
→- The rms current in the circuit.
- The rms potential difference across the capacitor, the resistor and the inductor. Note that the sum of the rms potential differences across the three elements is greater than the rms voltage of the source.
Figure shown a two slit arrangement with a source which emits unpolarised light. P is a polariser with axis whose direction is not given. If I0 is the intensity of the principal maxima when no polariser is present, calculate in the present case, the intensity of the principal maxima as well as of the first minima.
A neutron beam of energy E scatters from atoms on a surface with a spacing d = 0.1nm. The first maximum of intensity in the reflected beam occurs at θ = 30º. What is the kinetic energy E of the beam in eV?
In a simple Atwood machine, two unequal masses m1 and m2 are connected by a string going over a clamped light smooth pulley. In a typical arrangement m1 = 300g and m2 = 600g. The system is released from rest.
- Find the distance travelled by the first block in the first two seconds.
- Find the tension in the string.
- Find the force exerted by the clamp on the pulley.
A current i is passed through a silver strip of width d and area of cross-section A. The number of free electrons per unit volume is n.
- Find the drift velocity v of the electrons.
- If a magnetic field B exists in the region, as shown in the figure, what is the average magnetic force on the free electrons?
- Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor, which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will stop further accumulation of electrons.
- What will be the potential difference developed across the width of the conductor due to the electron-accumulation? The appearance of a transverse emf, when a current-carrying wire is placed in a magnetic field, is called Hall effect.
A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle θ with respect to the horizontal (Fig). The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.
