Taking incline plane as frame of reference,  Pseudo force ma act towards right.

component of Pseudo force up the incline is m.a.cos α which is balanced by m.g.sin α. so,

m.a.cos α = m.g.sin α

⇒a= g tan α

Using concept of Pseudo force

a= g tanθ

⇒ a = g tan 37 = 10 ×3/4= 7.5 m/s^2

Using Equation of motion

⇒Fnet = 10×2.5 = 25 N

Taking lift as frame of reference, T = mg +ma = mg (1 +a/g) = W (1+ a/g)

The condition to prevent the block from falling is that the friction force must be at least equal to the weight of the block:

$$f_s \geq mg$$

Since static friction is given by $f_s = \mu N$ and the normal force is due to pseudo force $N = ma$, we get:

$$\mu ma \geq mg$$

Dividing both sides by $\mu m$:

$$a \geq \frac{g}{\mu}$$

Thus, the required acceleration of the cart is $a \geq \frac{g}{\mu}$.

When the truck accelerates to the right with $a$, a pseudo force $ma$ acts to the left on the bob in the truck's frame. The bob reaches equilibrium where the tension components balance forces:

$$\tan \theta = \frac{\text{Pseudo force}}{\text{Weight}} = \frac{ma}{mg} = \frac{a}{g}$$ $$\theta = \tan^{-1} \left(\frac{a}{g} \right)$$

Thus, the pendulum tilts to the left at an angle $\theta = \tan^{-1}(a/g)$ with the vertical.

For the block to remain stationary relative to the wedge,

the component of  pseudo force up the incline balances the gravitational component along down the incline:

$$ma \cos \theta = mg \sin \theta$$

$$\mathrm{\Rightarrow \; a}=g\tan \theta$$

Assertion (A) is false. The Earth rotates and revolves, making a frame attached to it non-inertial. Reason (R) is false. Newton's laws in their original form are only valid in inertial frames. For a frame attached to the Earth, pseudo forces must be introduced to apply Newton's laws. Thus, both the Assertion and the Reason are false.

Assertion (A) is true. This is a fundamental statement of the Galilean principle of relativity. Reason (R) is true. The laws of physics are invariant in all inertial frames of reference. (R) correctly explains (A) because if physical laws are identical in all inertial frames, no internal experiment can distinguish between them.

Assertion (A) is true: When an elevator accelerates upwards with acceleration \(a\), the pseudo force on an object inside is \(ma\) downwards (in the non-inertial frame). So, for upward accelerating elevator, pseudo force on a block is downward.nReason (R) is false: Pseudo force is not a real force applied by the lift; it is an inertial force experienced in a non-inertial reference frame, acting opposite to the acceleration of the frame, not necessarily the direction of motion. Therefore, (A) is true but (R) is false.

Assertion (A) is true: If the elevator accelerates upwards, the apparent weight \(N = m(g+a)\) of the peanuts increases. If the moongphaliwala sells by the apparent weight reading (e.g., "1 kg" on the scale), they would be selling a *smaller actual mass* \(m_text{actual} = N/(g+a)\) for the same indicated weight. Thus, they gain more profit.

Reason (R) is true: When an elevator accelerates upwards, the normal force (apparent weight) on an object of mass \(m\) is \(N = m(g+a)\), which is greater than its actual weight \(mg\). Reason (R) correctly explains why the apparent weight increases, leading to the profit gain described in (A).