JEE Main 2024 · 1 Feb 2024 Shift 1

The dimensional formula of angular impulse is :

1. A[M L² T⁻²]
2. B[M L T⁻¹]
3. C[M L⁻² T⁻¹]
4. D[M L² T⁻¹]

A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle θ to the horizontal, the maximum height attained by it is equal to 4R. The angle of projection θ is then given by :

1. Acos⁻¹[(2gT²)/(π²R)]¹⁄²
2. Bsin⁻¹[(2gT²)/(π²R)]¹⁄²
3. Csin⁻¹[(π²R)/(2gT²)]¹⁄²
4. Dcos⁻¹[(πR)/(2gT²)]¹⁄²

A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass 10⁻² kg moving with a speed of 2 × 10² ms⁻¹. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use g = 10 m/s²)

1. A0.20 m
2. B0.30 m
3. C0.35 m
4. D0.40 m

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g = π² m/s², then the length of the second’s pendulum at a height h = 2R from the surface of earth will be, :

1. A2/9 m
2. B4/9 m
3. C8/9 m
4. D1/9 m

With rise in temperature, the Young’s modulus of elasticity :

1. Adecreases
2. Bincreases
3. Cremains unchanged
4. Dchanges erratically

The pressure and volume of an ideal gas are related as PV³⁄² = K (Constant). The work done when the gas is taken from state A (P₁, V₁, T₁) to state B (P₂, V₂, T₂) is :

1. A2 (P₂V₂ − P₁V₁)
2. B2 (P₂√V₂ − P₁√V₁)
3. C2 (P₁V₁ − P₂V₂)
4. D2 (√P₁V₁ − √P₂V₂)

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

1. A⁵⁄₂ R
2. B⁹⁄₄ R
3. C³⁄₂ R
4. D⁷⁄₄ R

Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

1. A½ CV²
2. B¼ CV²
3. C2 CV²
4. D¾ CV²